Solving Inequalities with Variables on Both Sides 2-5. Warm Up. Lesson Presentation Lesson Quiz
|
|
- Kerry Knight
- 5 years ago
- Views:
Transcription
1 Warm Up Lesson Presentation Lesson Quiz Holt Algebra McDougal 1 Algebra 1
2 Warm Up Solve each equation. 1. 2x = 7x + 15 x = y 21 = 4 2y y = (3z + 1) = 2(z + 3) z = (p 1) = 3p + 2 no solution 5. Solve and graph 5(2 b) > 5 2. b <
3 Objective Solve inequalities that contain variable terms on both sides.
4 Some inequalities have variable terms on both sides of the inequality symbol. You can solve these inequalities like you solved equations with variables on both sides. Use the properties of inequality to collect all the variable terms on one side and all the constant terms on the other side.
5 Example 1A: Variables on Both Sides Solve the inequality and graph the solutions. y 4y + 18 y 4y + 18 y y To collect the variable terms on one side, subtract y from both sides. 0 3y y 6 y (or y 6) Since 18 is added to 3y, subtract 18 from both sides to undo the addition. Since y is multiplied by 3, divide both sides by 3 to undo the multiplication
6 Example 1B: Variables on Both Sides Solve the inequality and graph the solutions. 4m 3 < 2m + 6 To collect the variable terms on one 2m 2m side, subtract 2m from both sides. 2m 3 < + 6 Since 3 is subtracted from 2m, add to both sides to undo the subtraction 2m < 9 Since m is multiplied by 2, divide both sides by 2 to undo the multiplication
7 Check It Out! Example 1a Solve the inequality and graph the solutions. 4x 7x + 6 4x 7x + 6 7x 7x To collect the variable terms on one side, subtract 7x from both sides. 3x 6 x 2 Since x is multiplied by 3, divide both sides by 3 to undo the multiplication. Change to
8 Solve the inequality and graph the solutions. 5t + 1 < 2t 6 5t + 1 < 2t 6 +2t +2t 7t + 1 < 6 1 < 1 7t < 7 7t < t < 1 Check It Out! Example 1b To collect the variable terms on one side, add 2t to both sides. Since 1 is added to 7t, subtract 1 from both sides to undo the addition. Since t is multiplied by 7, divide both sides by 7 to undo the multiplication
9 Example 2: Business Application The Home Cleaning Company charges $312 to power-wash the siding of a house plus $12 for each window. Power Clean charges $36 per window, and the price includes power-washing the siding. How many windows must a house have to make the total cost from The Home Cleaning Company less expensive than Power Clean? Let w be the number of windows.
10 Home Cleaning Company siding charge plus $12 per window Example 2 Continued w < 36 w w < 36w 12w 12w 312 < 24w 13 < w times # of windows is less than Power Clean cost per window times To collect the variable terms, subtract 12w from both sides. Since w is multiplied by 24, divide both sides by 24 to undo the multiplication. The Home Cleaning Company is less expensive for houses with more than 13 windows. # of windows.
11 Check It Out! Example 2 A-Plus Advertising charges a fee of $24 plus $0.10 per flyer to print and deliver flyers. Print and More charges $0.25 per flyer. For how many flyers is the cost at A-Plus Advertising less than the cost of Print and More? Let f represent the number of flyers printed. A-Plus Advertising fee of $24 plus $0.10 per flyer times # of flyers is less than Print and More s cost per flyer times # of flyers f < 0.25 f
12 Check It Out! Example 2 Continued f < 0.25f 0.10f 0.10f 24 < 0.15f To collect the variable terms, subtract 0.10f from both sides. Since f is multiplied by 0.15, divide both sides by 0.15 to undo the multiplication. 160 < f More than 160 flyers must be delivered to make A-Plus Advertising the lower cost company.
13 You may need to simplify one or both sides of an inequality before solving it. Look for like terms to combine and places to use the Distributive Property.
14 Example 3A: Simplify Each Side Before Solving Solve the inequality and graph the solutions. 2(k 3) > 6 + 3k 3 Distribute 2 on the left side of 2(k 3) > 3 + 3k the inequality. 2k + 2( 3) > 3 + 3k 2k 6 > 3 + 3k 2k 2k 6 > 3 + k > k To collect the variable terms, subtract 2k from both sides. Since 3 is added to k, subtract 3 from both sides to undo the addition.
15 Example 3A Continued 9 > k
16 Example 3B: Simplify Each Side Before Solving Solve the inequality and graph the solution. 0.9y 0.4y y 0.4y y 0.4y 0.5y y y 1 To collect the variable terms, subtract 0.4y from both sides. Since y is multiplied by 0.5, divide both sides by 0.5 to undo the multiplication
17 Check It Out! Example 3a Solve the inequality and graph the solutions. 5(2 r) 3(r 2) Distribute 5 on the left side of the 5(2 r) 3(r 2) inequality and distribute 3 on the right side of the inequality. 5(2) 5(r) 3(r) + 3( 2) 10 5r 3r r 3r + 5r +5r 16 8r Since 6 is subtracted from 3r, add 6 to both sides to undo the subtraction. Since 5r is subtracted from 16 add 5r to both sides to undo the subtraction.
18 Check It Out! Example 3a Continued 16 8r 2 r Since r is multiplied by 8, divide both sides by 8 to undo the multiplication
19 Check It Out! Example 3b Solve the inequality and graph the solutions. 0.5x x < 0.3x x 0.3 < 0.3x x 0.3 < 0.3x x < 0.3x x 0.3x 2.1x < 6.3 x < 3 Simplify. Since 0.3 is subtracted from 2.4x, add 0.3 to both sides. Since 0.3x is added to 6.3, subtract 0.3x from both sides. Since x is multiplied by 2.1, divide both sides by 2.1.
20 Check It Out! Example 3b Continued x <
21 Some inequalities are true no matter what value is substituted for the variable. For these inequalities, all real numbers are solutions. Some inequalities are false no matter what value is substituted for the variable. These inequalities have no solutions. If both sides of an inequality are fully simplified and the same variable term appears on both sides, then the inequality has all real numbers as solutions or it has no solutions. Look at the other terms in the inequality to decide which is the case.
22 Additional Example 4A: All Real Numbers as Solutions or No Solutions Solve the inequality. 2x x The same variable term (2x) appears on both sides. Look at the other terms. For any number 2x, subtracting 7 will always result in a lower number than adding 5. All values of x make the inequality true. All real numbers are solutions.
23 Additional Example 4B: All Real Numbers as Solutions or No Solutions Solve the inequality. 2(3y 2) 4 3(2y + 7) 6y 8 6y + 21 Distribute 2 on the left side and 3 on the right side and combine like terms. The same variable term (6y) appears on both sides. Look at the other terms. For any number 6y, subtracting 8 will never result in a higher number than adding 21. No values of y make the inequality true. There are no solutions.
24 Check It Out! Example 4a Solve the inequality. 4(y 1) 4y + 2 4y 4 4y + 2 Distribute 4 on the left side. The same variable term (4y) appears on both sides. Look at the other terms. For any number 4y, subtracting 4 will never result in a higher number than adding 2. No values of y make the inequality true. There are no solutions.
25 Check It Out! Example 4b Solve the inequality. x 2 < x + 1 The same variable term (x) appears on both sides. Look at the other terms. For any number x, subtracting 2 will always result in a lesser number than adding 1. All values of x make the inequality true. All real numbers are solutions.
26 Lesson Quiz: Part I Solve each inequality and graph the solutions. 1. t < 5t + 24 t > x 9 4.1x 81 x b + 4(1 b) > b 9 b < 13
27 Lesson Quiz: Part II 4. Rick bought a photo printer and supplies for $186.90, which will allow him to print photos for $0.29 each. A photo store charges $0.55 to print each photo. How many photos must Rick print before his total cost is less than getting prints made at the photo store? Rick must print more than 718 photos.
28 Lesson Quiz: Part III Solve each inequality. 5. 2y 2 2(y + 7) no solutions 6. 2( 6r 5) < 3(4r + 2) all real numbers
4-7 Point-Slope Form. Warm Up Lesson Presentation Lesson Quiz
Warm Up Lesson Presentation Lesson Quiz Holt Algebra McDougal 1 Algebra 1 Warm Up Find the slope of the line containing each pair of points. 1. (0, 2) and (3, 4) 2. ( 2, 8) and (4, 2) 1 3. (3, 3) and (12,
More informationSolving Inequalities with Variables on Both Sides
Warm Up Lesson Presentation Lesson Quiz 1 Section 3-5 1 2 pts Bell Quiz 3-5 Solve each equation. 1. 2x = 7x + 15 3 pts 2. Solve and graph 5(2 b) > 5 2. 5 pts possible Section 3-5 2 Questions on 3-4 Section
More information2-3. Warm Up Lesson Presentation Lesson Quiz. Holt Algebra McDougal 1 Algebra 1
Warm Up Lesson Presentation Lesson Quiz Holt Algebra McDougal 1 Algebra 1 Warm Up Solve each equation. 1. 5a = 30 6 2. 10 3. 4. Graph each inequality. 5. x 10 6. x < 3 Objectives Solve one-step inequalities
More information4-2 Using Intercepts. Warm Up Lesson Presentation Lesson Quiz
4-2 Using Intercepts Warm Up Lesson Presentation Lesson Quiz Holt Algebra McDougal 1 Algebra 1 Warm Up Solve each equation. 1. 5x + 0 = 10 2 2. 33 = 0 + 3y 11 3. 1 4. 2x + 14 = 3x + 4 2 5. 5y 1 = 7y +
More informationProperties of Logarithms
Properties of Logarithms Warm Up Lesson Presentation Lesson Quiz Algebra 2 Warm Up Simplify. 1. (2 6 )(2 8 ) 2 14 2. (3 2 )(3 5 ) 3 3 3 8 3. 4. 4 4 5. (7 3 ) 5 7 15 Write in exponential form. 6. log x
More informationQuick Answers - Chapter : Relations and Functions: Check for Understanding
of 38 9/5/2012 8:07 AM Quick Answers - Chapter 1 1-1: Relations and Functions: Check for Understanding 1. 9. 2. 10. 11. 3. 12. 13. 4. 14. 15. of 38 9/5/2012 8:07 AM 5. 16. 6. 7. 8. 1-1: Relations and Functions:
More informationSolving Two-Step Inequalities
Practice A Solving Two-Step Inequalities Solve and graph each inequality. 1. 3x + 4 < 13 2. 2x 5 > 3 _ 3. x + 2 4 1 4. x + 6 3 < 2 _ 5. 9x + 8 35 6. x 5 7 < 6 _ 7. Maria works for a magazine, and she wants
More informationLesson 1 6. Algebra: Variables and Expression. Students will be able to evaluate algebraic expressions.
Lesson 1 6 Algebra: Variables and Expression Students will be able to evaluate algebraic expressions. P1 Represent and analyze patterns, rules and functions with words, tables, graphs and simple variable
More informationWarm Up. Solve each equation. Check your answer. 1. 6x = m = y =18.4
Warm Up Solve each equation. Check your answer. 1. 6x = 36 6 2. 3. 5m = 18 4. 48 3.6 63 5. 8y =18.4 2.3 Write and use ratios, rates, and unit rates. Write and solve proportions. Objectives Key Concepts
More informationAim #35.1: How do we graph using a table?
A) Take out last night's homework Worksheet - Aim 34.2 B) Copy down tonight's homework Finish aim 35.1 Aim #35.1: How do we graph using a table? C) Plot the following points... a) (-3, 5) b) (4, -2) c)
More informationE. Slope-Intercept Form and Direct Variation (pp )
and Direct Variation (pp. 32 35) For any two points, there is one and only one line that contains both points. This fact can help you graph a linear equation. Many times, it will be convenient to use the
More informationMathematics Success Grade 8
Mathematics Success Grade 8 T429 [OBJECTIVE] The student will solve systems of equations by graphing. [PREREQUISITE SKILLS] solving equations [MATERIALS] Student pages S207 S220 Rulers [ESSENTIAL QUESTIONS]
More information1Solve linear. 2Solve linear. Then. Now. Why?
Solving Multi-Step Inequalities Then You solved multistep equations. (Lesson 2-3) Now 1Solve linear inequalities involving more than one operation. 2Solve linear inequalities involving the Distributive
More informationSolving Linear & Graphing Inequalities
Solving Linear & Graphing Inequalities Sep 7 11:06 PM 1 Open circle on the graph means that the inequality will be greater than or less than. > or < Closed circle on the graph means that the inequality
More informationInvestigating Intercepts
Unit: 0 Lesson: 01 1. Can more than one line have the same slope? If more than one line has the same slope, what makes the lines different? a. Graph the following set of equations on the same set of aes.
More informationHonors Algebra 2 w/ Trigonometry Chapter 14: Trigonometric Identities & Equations Target Goals
Honors Algebra w/ Trigonometry Chapter 14: Trigonometric Identities & Equations Target Goals By the end of this chapter, you should be able to Identify trigonometric identities. (14.1) Factor trigonometric
More informationAlgebra 1 Online:
Dear Algebra 2 Students, Within this packet you will find mathematical concepts and skills learned in Algebra 1 that are the foundation from which Algebra 2 is built. These concepts need to be reviewed
More informationGraphs, Linear Equations and Functions
Graphs, Linear Equations and Functions There are several ways to graph a linear equation: Make a table of values Use slope and y-intercept Use x and y intercepts Oct 5 9:37 PM Oct 5 9:38 PM Example: Make
More informationLesson Plans for Christy Dempsey, Tippit Middle School Week of Monday, November 07, 2016 Monday, November 07, 2016 Day 52
Lesson Plans for Christy Dempsey, Tippit Middle School Week of Monday, November 07, 2016 Monday, November 07, 2016 affect linear and area measurements. figure with changes in dimensions. How can proportional
More informationSlopes of of Parallel and and Perpendicular Lines Lines Holt Algebra 1
5-8 Slopes of of Parallel and and Lines Warm Up Lesson Presentation Lesson Quiz Bell Quiz 5-8 Find the reciprocal. 1. 2 2. 1 pt 1 pt 1 pt 3. 2 pts 2 pts 2 pts Find the slope of the line that passes through
More informationLesson 11: Linear Functions, Part 2
Lesson 11 continues the study of linear functions. In this lesson, we look at how to write linear equations in slope-intercept and general form and applications where these may be used. We also look at
More informationStudy Guide For use with pages
3.1 GOAL For use with pages 119 124 Solve two-step equations. EXAMPLE 1 Using Subtraction and Division to Solve Solve 14 x 12 54. Check your solution. 14x 12 54 Write original equation. 14x 12 12 54 12
More information2.3 BUILDING THE PERFECT SQUARE
16 2.3 BUILDING THE PERFECT SQUARE A Develop Understanding Task Quadratic)Quilts Optimahasaquiltshopwhereshesellsmanycolorfulquiltblocksforpeoplewhowant tomaketheirownquilts.shehasquiltdesignsthataremadesothattheycanbesized
More informationYou found trigonometric values using the unit circle. (Lesson 4-3)
You found trigonometric values using the unit circle. (Lesson 4-3) LEQ: How do we identify and use basic trigonometric identities to find trigonometric values & use basic trigonometric identities to simplify
More informationLINEAR EQUATIONS IN TWO VARIABLES
LINEAR EQUATIONS IN TWO VARIABLES What You Should Learn Use slope to graph linear equations in two " variables. Find the slope of a line given two points on the line. Write linear equations in two variables.
More informationLesson 6.1 Linear Equation Review
Name: Lesson 6.1 Linear Equation Review Vocabulary Equation: a math sentence that contains Linear: makes a straight line (no Variables: quantities represented by (often x and y) Function: equations can
More informationMath 154 :: Elementary Algebra
Math :: Elementary Algebra Section 9. Section 9. Section 9. Section 9. Section 9. Section 9.6 Math :: Elementary Algebra Section 9. Introduction to Square Roots. This answer should be in your own words..
More informationRadical Expressions and Graph (7.1) EXAMPLE #1: EXAMPLE #2: EXAMPLE #3: Find roots of numbers (Objective #1) Figure #1:
Radical Expressions and Graph (7.1) Find roots of numbers EXAMPLE #1: Figure #1: Find principal (positive) roots EXAMPLE #2: Find n th roots of n th powers (Objective #3) EXAMPLE #3: Figure #2: 7.1 Radical
More informationA slope of a line is the ratio between the change in a vertical distance (rise) to the change in a horizontal
The Slope of a Line (2.2) Find the slope of a line given two points on the line (Objective #1) A slope of a line is the ratio between the change in a vertical distance (rise) to the change in a horizontal
More informationALGEBRA 2 ~ Lessons 1 13
ALGEBRA 2 ~ Lessons 1 13 Remember to write the original problem and show all of your steps! All work should be done on a separate piece of paper. ASSIGNMENT 1 Arithmetic (No calculator.) Add, subtract
More informationUsing Slopes and Intercepts
CODE Name Date Teacher Practice A Using Slopes and Intercepts 1. Name the ordered pair if the x-intercept is 2. 2. Name the ordered pair if the y-intercept is 8. 3. In the ordered pair (9, 0), what is
More informationComparing Exponential and Logarithmic Rules
Name _ Date Period Comparing Exponential and Logarithmic Rules Task : Looking closely at exponential and logarithmic patterns ) In a prior lesson you graphed and then compared an exponential function with
More informationLesson 1 Area of Parallelograms
NAME DATE PERIOD Lesson 1 Area of Parallelograms Words Formula The area A of a parallelogram is the product of any b and its h. Model Step 1: Write the Step 2: Replace letters with information from picture
More informationLearn to solve multistep equations.
Learn to solve multistep equations. Levi has half as many comic books as Jamal has. If you add 6 to the number of comic books Jamal has and then divide by 7, you get the number of comic books Brooke has.
More informationAlgebra Success. LESSON 16: Graphing Lines in Standard Form. [OBJECTIVE] The student will graph lines described by equations in standard form.
T328 [OBJECTIVE] The student will graph lines described by equations in standard form. [MATERIALS] Student pages S125 S133 Transparencies T336, T338, T340, T342, T344 Wall-size four-quadrant grid [ESSENTIAL
More informationChapter 01 Test. 1 Write an algebraic expression for the phrase the sum of g and 3. A 3g B 3g + 3 C g 3 D g Write a word phrase for.
hapter 01 Test Name: ate: 1 Write an algebraic expression for the phrase the sum of g and 3. 3g 3g + 3 g 3 g + 3 2 Write a word phrase for. negative 5 minus 4 plus a number n negative 5 minus 4 times a
More informationMath 138 Exam 1 Review Problems Fall 2008
Chapter 1 NOTE: Be sure to review Activity Set 1.3 from the Activity Book, pp 15-17. 1. Sketch an algebra-piece model for the following problem. Then explain or show how you used it to arrive at your solution.
More informationOutcome 9 Review Foundations and Pre-Calculus 10
Outcome 9 Review Foundations and Pre-Calculus 10 Level 2 Example: Writing an equation in slope intercept form Slope-Intercept Form: y = mx + b m = slope b = y-intercept Ex : Write the equation of a line
More informationConcept: Solving Multi-Step Equations
Concept: Solving Multi-Step Equations Warm Up Name: Recall: A two-step equation requires 2 operations in order to isolate and solve for the variable. Solve each two-step equation below. Show all your steps.
More informationconstant EXAMPLE #4:
Linear Equations in One Variable (1.1) Adding in an equation (Objective #1) An equation is a statement involving an equal sign or an expression that is equal to another expression. Add a constant value
More informationSect 4.5 Inequalities Involving Quadratic Function
71 Sect 4. Inequalities Involving Quadratic Function Objective #0: Solving Inequalities using a graph Use the graph to the right to find the following: Ex. 1 a) Find the intervals where f(x) > 0. b) Find
More information3-5 Slopes of Lines. Warm Up Lesson Presentation Lesson Quiz. Holt McDougal Geometry
3-5 Slopes of Lines Warm Up Lesson Presentation Lesson Quiz Geometry Warm Up Find the value of m. 1. 2. 3. 4. undefined 0 Objectives Find the slope of a line. Use slopes to identify parallel and perpendicular
More informationSect Linear Equations in Two Variables
99 Concept # Sect. - Linear Equations in Two Variables Solutions to Linear Equations in Two Variables In this chapter, we will examine linear equations involving two variables. Such equations have an infinite
More information5-2 Using Intercepts. Warm Up. Solve each equation. 1. 5x + 0 = = 0 + 3y. 4. 2x + 14 = 3x y 1 = 7y + 5
Warm Up Solve each equation. 1. 5x + 0 = 10 2. 33 = 0 + 3y 3. 4. 2x + 14 = 3x + 4 5. 5y 1 = 7y + 5 Learning Goals 1. The student is able to find x and y-intercepts 2. The student is able to identify meanings
More informationMath 1023 College Algebra Worksheet 1 Name: Prof. Paul Bailey September 22, 2004
Math 1023 College Algebra Worksheet 1 Name: Prof. Paul Bailey September 22, 2004 Every vertical line can be expressed by a unique equation of the form x = c, where c is a constant. Such lines have undefined
More informationCK-12 Algebra II with Trigonometry Concepts 1
1.1 Subsets of Real Numbers 1. Rational Number. Irrational Number. Rational Number 4. Whole Number 5. Integer 6. Irrational Number 7. Real, Rational, Integer, Whole, and Natural Number 8. Real and Rational
More informationNOTES: SIGNED INTEGERS DAY 1
NOTES: SIGNED INTEGERS DAY 1 MULTIPLYING and DIVIDING: Same Signs (POSITIVE) + + = + positive x positive = positive = + negative x negative = positive Different Signs (NEGATIVE) + = positive x negative
More informationSolving Equations and Graphing
Solving Equations and Graphing Question 1: How do you solve a linear equation? Answer 1: 1. Remove any parentheses or other grouping symbols (if necessary). 2. If the equation contains a fraction, multiply
More information1.7 Parallel and Perpendicular Lines
Section 1.7 Parallel and Perpendicular Lines 11 Eplaining the Concepts 17. Name the five forms of equations of lines given in this section. 18. What tpe of line has one -intercept, but no -intercept? 19.
More informationCourse Syllabus - Online Prealgebra
Week 1 Week 2 Week 3 Week 4 Week 5 Week 6 1.1 Whole Numbers, Place Value Practice Problems for section 1.1 HW 1A 1.2 Adding Whole Numbers Practice Problems for section 1.2 HW 1B 1.3 Subtracting Whole Numbers
More information2-6 Rates, Ratios, and Proportions. Warm Up. Solve each equation. Check your answer. 1. 6x = m = y =18.4 Multiply
Warm Up Solve each equation. Check your answer. 1. 6x = 36 2. 3. 5m = 18 4. 5. 8y =18.4 Multiply. 6. 7. Learning Goals 1. Students will identify important information from an application problem and use
More informationBIG IDEA 1: Develop an understanding of and fluency with multiplication and division of fractions and decimals BIG IDEA 1:
BIG IDEA 1: Develop an understanding of and fluency with multiplication and division of fractions and decimals Multiplying and Dividing Decimals Explain the difference between an exact answer and an estimated
More informationReady To Go On? Skills Intervention 14-1 Graphs of Sine and Cosine
14A Ready To Go On? Skills Intervention 14-1 Graphs of Sine and Cosine Find these vocabulary words in Lesson 14-1 and the Multilingual Glossary. Vocabulary periodic function cycle period amplitude frequency
More informationPart I: Bell Work When solving an inequality, when would you flip the inequality sign?
Algebra 135 Seminar Lesson 55 Part I: Bell Work When solving an inequality, when would you flip the inequality sign? Part II: Mini-Lesson Review for Ch 6 Test Give a review lesson for the Chapter 6 test.
More informationPractice A. Solving Inequalities by Adding or Subtracting. Solve. Then match each solution set with its graph. 1. r 1 2 A. 2. m 3 6 B. 3. x 4 1 C.
Practice A Solving Inequalities by Adding or Subtracting Solve. Then match each solution set with its graph. 1. r 1 2 A. 2. m 3 6 B. 3. x 4 1 C. 4. k 2 5 D. Solve. Check each answer. 5. a 7 2 6. h 9 3
More informationPre-Algebra Unit 1: Number Sense Unit 1 Review Packet
Pre-Algebra Unit 1: Number Sense Unit 1 Review Packet Target 1: Writing Repeating Decimals in Rational Form Remember the goal is to get rid of the repeating decimal so we can write the number in rational
More informationWelcome Accelerated Algebra 2!
Welcome Accelerated Algebra 2! Tear-Out: Pgs. 348-354 (classwork) Pg. 355 (homework) U5H6: Pg. 355 #7-9, 11-12,14-16, 18-23 Updates: U5Q2 will be January 30 th U5T will be February 6 th Agenda (1) Warm-Up!
More informationLesson 1b Linear Equations
In the first lesson we looked at the concepts and rules of a Function. The first Function that we are going to investigate is the Linear Function. This is a good place to start because with Linear Functions,
More information16. Two years of local Internet service costs $685, including the installation fee of $85. What is the monthly fee?
Solving Two-Step Equations 11.1 Check each answer. 1. 7x 8 36 2. 3y 7 2 3. 4a 13 19 4. 6a 4 2 5. 5k 2 6 6. 9m 14 8 7. v 4 3 5 8. u 5 3 1 9. 6 z 9 9 10. 7 f 2 1 11. 9 w 4 5 12. e 7 3 5 13. 8 d 5 2 14. u
More informationSummer Work Packet For Students Entering Algebra 1 Honors
June 2017 Summer Work Packet For Students Entering Algebra 1 Honors Dear Student, Welcome! I have prepared a summer work packet for you to help you better prepare for your upcoming course, Algebra 1 Honors.
More information6.1.3 Where do the solutions begin and end?
6.1.3 Where do the solutions begin and end? One Variable Inequalities Word
More informationSquare Roots and the Pythagorean Theorem
UNIT 1 Square Roots and the Pythagorean Theorem Just for Fun What Do You Notice? Follow the steps. An example is given. Example 1. Pick a 4-digit number with different digits. 3078 2. Find the greatest
More informationWelcome to Norwalk High School!
Welcome to Norwalk High School! You are about to embark on the next journey in your educational career. We are looking forward to a year-long adventure with you in Algebra. There are a team of teachers
More informationIntegrated Math 1 - Chapter 4 Practice Work
Name Core Date Lesson 4.1.1 Finding Connections Between Representations 4-3. On graph paper, draw Figure 0 and Figure 4 for the pattern at right. Represent the number of tiles in each figure in an x y
More informationSlope. Domain 2 Lesson 11. Getting the Idea
Domain Lesson Slope Common Core Standard: 8.EE. Getting the Idea The graph of a linear equation is a straight line. The steepness of the line is called its slope. The slope shows the rate at which two
More informationThe Fundamental Counting Principle
LESSON 10-6 The Fundamental Counting Principle Lesson Objectives Find the number of possible outcomes in an experiment Vocabulary Fundamental Counting Principle (p. 558) tree diagram (p. 559) Additional
More informationKeystone Exams: Algebra I Assessment Anchors and Eligible Content. Pennsylvania Department of Education
Keystone Exams: Algebra I Assessment Anchors and Pennsylvania Department of Education www.education.state.pa.us 2010 PENNSYLVANIA DEPARTMENT OF EDUCATION General Introduction to the Keystone Exam Assessment
More informationSolving Rational Equations
Solving Rational Equations Return to Table of Contents 74 Solving Rational Equations Step 1: Find LCD Step 2: Multiply EACH TERM by LCD Step 3: Simplify Step 4: Solve Teacher Notes Step 5: Check for Extraneous
More informationAddition and Subtraction of Polynomials
Student Probe What is 10x 2 2y x + 4y 6x 2? Addition and Subtraction of Polynomials Answer: 4x 2 x + 2y The terms 10x 2 and - 6x 2 should be combined because they are like bases and the terms - 2y and
More informationWe can see from columns 1 and 2 that: [Bottom number 12 = Top number] OR. [Top number 12 = Bottom number] [132] [6] 11 [10]
Q1-3. To complete the table, pick a column where you have been given both the top and the bottom numbers. Work out the relationship between the top and the bottom number. Apply the same rule to all columns.
More informationOperations and Algebraic Thinking
Lesson 1 Operations and Algebraic Thinking Name Use Color Tiles to build each array. Write the multiplication sentence for each array. 1. 2. 3. rows of tiles rows of tiles rows of tiles Build each array
More information2. Questions on Classwork and Homework form yesterday. 4. Completing the square to solve quadratic
1. Warm -up word problem - 2. Questions on Classwork and Homework form yesterday 3. Number Sense. 4. Completing the square to solve quadratic equations 1 2 3 Apr 12 12:35 PM 4 Apr 13 2:12 PM 5 6 7 factors
More informationAlgebra EOC Practice Test #3
Class: Date: Algebra EOC Practice Test #3 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Write the monomial 4x 2 y 3y 3 without the use of negative exponents.
More informationPractice 6 4 Point Slope Form And Writing Linear Equation Answer Key
Practice 6 4 Point Slope Form And Writing Linear Equation Answer Key Free PDF ebook Download: Practice 6 4 Point Slope Form And Writing Linear Equation Answer Key Download or Read Online ebook practice
More informationMath Exam 1 Review Fall 2009
Note: This is NOT a practice exam. It is a collection of problems to help you review some of the material for the exam and to practice some kinds of problems. This collection is not necessarily exhaustive.
More informationSection 3.5. Equations of Lines
Section 3.5 Equations of Lines Learning objectives Use slope-intercept form to write an equation of a line Use slope-intercept form to graph a linear equation Use the point-slope form to find an equation
More informationStudy Guide: Solving Equations and Inequalities
Please complete this study guide and submit it when you take your test. If you have questions, please make sure you ask me before December 5!! Solving Equations Your goal in solving equations is to get
More informationPart Mark Answer Further Information. Part Mark Answer Further Information Award 1 mark for 20, 15, 35 or. Part Mark Answer Further Information
Cambridge International Examinations Cambridge Checkpoint MATHEMATICS 1112/01 Paper 1 For Examination from 2014 SPECIMEN MARK SCHEME MAXIMUM MARK: 50 This document consists of 11 printed pages and 1 blank
More informationCK-12 Geometry Inductive Reasoning
CK-12 Geometry Inductive Reasoning Learning Objectives Recognize visual and number patterns. Extend and generalize patterns. Write a counterexample. Review Queue a. Look at the patterns of numbers below.
More informationTenMarks Curriculum Alignment Guide: EngageNY/Eureka Math, Grade 7
EngageNY Module 1: Ratios and Proportional Relationships Topic A: Proportional Relationships Lesson 1 Lesson 2 Lesson 3 Understand equivalent ratios, rate, and unit rate related to a Understand proportional
More informationLearning Log Title: CHAPTER 6: DIVIDING AND BUILDING EXPRESSIONS. Date: Lesson: Chapter 6: Dividing and Building Expressions
Chapter 6: Dividing and Building Epressions CHAPTER 6: DIVIDING AND BUILDING EXPRESSIONS Date: Lesson: Learning Log Title: Date: Lesson: Learning Log Title: Chapter 6: Dividing and Building Epressions
More informationDIVISION BY FRACTIONS
DIVISION BY FRACTIONS 6.. 6.. Division by fractions introduces three methods to help students understand how dividing by fractions works. In general, think of division for a problem like 8 as, In 8, how
More information3-6. Lines in the Coordinate Plane Going Deeper E X A M P L E. Slope-Intercept Form. Point-Slope Form. Writing Equations of Parallel Lines
Name Class Date 3-6 Lines in the Coordinate Plane Going Deeper Essential question: How can you use slope to write equations of lines that are parallel or perpendicular? Recall that a linear function can
More information15 x 15 Multiplication Tables (Blank) X
15 x 15 Multiplication Tables (Blank) X 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 15 x 15 Multiplication Tables (Completed) X 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 1 2 3 4
More informationUse Algebra to Solve Word Problems
Domain 3 Lesson 17 Use Algebra to Solve Word Problems Common Core Standards: 7.EE.3, 7.EE.4.a Getting the Idea One way to solve a word problem is arithmetically. Problem solving strategies can help you
More informationLesson 4.6 Best Fit Line
Lesson 4.6 Best Fit Line Concept: Using & Interpreting Best Fit Lines EQs: -How do we determine a line of best fit from a scatter plot? (S.ID.6 a,c) -What does the slope and intercept tell me about the
More informationChange Standard Form To Slope Intercept Kuta
Change Standard To Slope Intercept Kuta Free PDF ebook Download: Change Standard To Slope Intercept Kuta Download or Read Online ebook change standard form to slope intercept kuta in PDF at From The Best
More informationChapter 4. Lesson Lesson The parabola should pass through the points (0, 0) and (2, 0) and have vertex (1, 1).
Chapter 4 Lesson 4.1.1 4-3. The parabola should pass through the points (0, 0) and (2, 0) and have vertex (1, 1). 4-4. She should have received two sports cars and ten pieces of furniture. 4-5. 1 3 ( 2x)=
More informationx < 7 x > 3 x 9 2x - 6 = x = 4 3x = x = x = -2 x = 7 5x + 8 > 23 2x 4 14 x + 3 < NOTES Solving Multi Step Inequalities
BELLWORK: Solve each equation. A) x 16 = 12 B) 3x + 5 = 1 C) 2(x 3) = 8 +16 +16 x = 4-5 -5 3x = -6 3 3 x = -2 2x - 6 = 8 +6 +6 2x = 14 2 2 x = 7 LESSON 2. 4 - Solving Multi-Step Inequalities Works very
More informationName Date Class. When solving multi-step equations, first combine like terms on each side if possible. Then use inverse operations.
x-x 1-x 1-4 Solving Two-Step and Multi-Step Equations When solving multi-step equations, first combine like terms on each side if possible. Then use inverse operations. 4x 3 15 Operations x is multiplied
More informationSecond Practice Test 1 Level 5-7
Mathematics Second Practice Test 1 Level 5-7 Calculator not allowed Please read this page, but do not open your booklet until your teacher tells you to start. Write your name and the name of your school
More informationName: Date: Chapter 2 Quiz Geometry. Multiple Choice Identify the choice that best completes the statement or answers the question.
Name: Date: Chapter 2 Quiz Geometry Multiple Choice Identify the choice that best completes the statement or answers the question. 1. What is the value of x? Identify the missing justifications.,, and.
More informationVariables and expressions Block 1 Student Activity Sheet
Block 1 Student Activity Sheet 1. Record your understandings of key vocabulary for this topic. Vocabulary term My understanding of what the term means Examples that show the meaning of the term. a. Variable
More informationPerry High School. Algebra 2: Week 9. Note: Don t forget to read the sections before or after we cover them. Also, don t forget the website.
Algebra 2: Week 9 Monday: 2.8 Absolute Value Functions Tuesday: 2.8 Work Day Wednesday: Review Exam 2, Day 1 Thursday: Professional Day, NO SCHOOL Friday: Fall Break? NO SCHOOL Note: Don t forget to read
More informationPractice A. Summer Income Use the following information. Decide which of the,two points 'lies on the graph of the line.
NAME ~ ~ _ DATE Practice A For use withpages 216-217 Decide which of the,two points 'lies on the graph of the line. 1. x + Y = 8 2. 2x + Y = 8 3. Y - x = 2 a. (2,4) b. (2,6) a. (2,2) b. (3,2) a. (5, 3)
More information2 Reasoning and Proof
www.ck12.org CHAPTER 2 Reasoning and Proof Chapter Outline 2.1 INDUCTIVE REASONING 2.2 CONDITIONAL STATEMENTS 2.3 DEDUCTIVE REASONING 2.4 ALGEBRAIC AND CONGRUENCE PROPERTIES 2.5 PROOFS ABOUT ANGLE PAIRS
More information2. Three times Antonio s age plus five times Sarah s age equals 43. Sarah s age is also eight times Antonio s age. How old is Sarah?
Name: Block: Date: Study Guide 1. The math club sells candy bars and drinks during football games. 50 candy bars and 100 drinks will sell for $275. 130 candy bars and 80 drinks will sell for $265. How
More information1.) Write the equation for the balance shown below. 3.) Draw a balance for the following equation. 5x + 1 = 3x + 15
1.) Write the equation for the balance shown below. 2.) Solve for the number of blocks in a bag. 3.) Draw a balance for the following equation. 5x + 1 = 3x + 15 Warm Up Wobble chairs go to: Kayden, Bailey,
More informationGraphical Inequalities
Graphical Inequalities Question Paper 5 Level IGCSE Subject Maths (0580) Exam Board Cambridge International Examinations (CIE) Paper Type Extended Topic Algebra and graphs Sub-Topic Graphical Inequalities
More information7.4, 9.42, 55,
Good Luck to: Period: Date DIRECTIONS: Show all work in the space provided. 1. Which of the following equations is equivalent to: 2 1 3 x + 3 2 a. 7x + 18 7 b. 3 x + 18 c. 2.3x + 4.2 d. 2.13x + 4.2 2.
More information