Solving Two-Step Inequalities

Transcription

1 Practice A Solving Two-Step Inequalities Solve and graph each inequality. 1. 3x + 4 < x 5 > 3 _ 3. x x < 2 _ 5. 9x x 5 7 < 6 _ 7. Maria works for a magazine, and she wants to earn at least $2,000 this month. She earns $750 as a base salary plus $50 for each membership sold. Write an inequality to show how many memberships Maria will have to sell in order to reach her goal.

2 Practice B Solving Two-Step Inequalities Solve and graph each inequality. 1. 8x x _ 3. x > 4 4. x < 5 _ 5. x x 4 < 1 _ 7. An insurance company wants their profit to be no less than $10,000 this month. The company earns a profit of $4,000 for having a license to sell insurance plus $250 for each policy sold. How many policies will the company have to sell in order to reach their goal?

3 Practice C Solving Two-Step Inequalities Solve and graph each inequality. 1. 6x 17 > x 9 25 _ 3. x > 2 4. x _ Write a two-step inequality for each sentence. Then solve the inequality. 5. Three times a number minus seven 6. A number divided by four, plus five is greater than negative four. is less than or equal to seven. _ 7. A local print shop cannot print more than 5,500 pages in one day. The shop acquired a print job of 3,250 pages in the morning. Another smaller print job has 15 pages per booklet. How many booklets can the print shop print before the end of the day?

4 Review for Mastery Solving Two-Step Inequalities When solving a two-step inequality, you will need to undo two operations. This is exactly like undoing operations for two-step equations. 2x 5 > 7 2x > Undo 5 by adding 5 to both sides of the inequality 2x > 12 2x 2 > 12 2 x > 6 Undo 2 by dividing both sides by 2 When you have solved the inequality, you can draw the solution on a number line as you learned to do in the previous section. Since x is strictly greater than 6, the number line should have an open circle over the 6 and a dark arrow pointing to the right. Solve and graph each inequality. 1. 7x x + 4 < 6 _ 3. 8x + 7 > x _

5 Name Date Class Challenge Inequalities With Two Variables You can determine if an ordered pair is a solution of an inequality by substituting the values into the inequality. If the inequality is true, the ordered pair is a solution of the inequality. If the inequality is false, the ordered pair is not a solution of the inequality. Example: Is (1, 6) or (2, 3) a solution of the inequality y < x + 5? (1, 6) y < x + 5 (2, 3) y < x + 5 Solve. 6 < (1) < (2) < 6 False 3 < 7 True (1, 6) is not a solution. (2, 3) is a solution. 1. Which of the following ordered pairs are solutions of y 2x 7. (1, 5), (1, 0), (3, 7), (2, 4)? 2. Which of the following ordered pairs are solutions of y > 3 x. ( 3, 0), (1, 5), (3, 1), (5, 2)? 3. Which of the following ordered pairs are solutions of 7y 2x < 13. ( 4, 0), (0, 2), (4, 3), (6, 3)? 4. For the inequality y 8 + 2x, let x = 6. Solve for y. 5. List 4 ordered pairs that are solutions to y 8x List 4 ordered pairs that are solutions of y 6x 10.

6 Problem Solving Solving Two-Step Inequalities Write an inequality and then solve. 1. Nancy s distances on four long-jumps were 49 inches, 52 inches, 47 inches, and 50 inches. What distance must Nancy jump to ensure an average distance of at least 50 inches? 2. A lunchroom can hold no more than 415 people. The lunch tables will hold 160 people. The committee is setting up 15 rows of chairs. What is the greatest number that can be in each row? 3. A scout troop sells cans of popcorn. They will receive 45% of their total sales, and they are giving away $30 of popcorn in samples. If the troop wants to make at least $420, what must their total sales be? Solve each problem. 4. Ron wants to give away at least $160. He plans give away $20 per week. He already gave away $30. Which inequality can he use to find how many weeks to reach his goal? A w 160 B w 160 C w < 160 D w > A store sells hats for $10. The store pays $6 per hat and bought an embroidery machine for $72 to customize each hat. How many hats must they sell to make a profit? A 4 C 16 B 8 D Rusty paid a $12 one-time fee for a website membership. The monthly fee is $3. If he has $35 to spend, which inequality can he use to find how many months can he belong? F m 35 G m 35 H m < 35 J m > Terry earned an 88, 79, 86, and a 90 on four math tests. What does she need to earn on the fifth test to have at least an 87 average? F 82 H 89 G 86 J 92

7 Reading Strategies The Language of Inequalities The following list shows some common phrases used in word problems and how they translate into inequality symbols. Symbol Phrase < less than at most no more than cannot exceed > greater than at least no less than must exceed Use the table to complete each description to match the inequality x Bob has to take three math tests. What must he make on 80 3 the third test so that his average is 80? 2. 2x For a football game you spent $15 on tickets, and you want to buy two t-shirts. How much can you spend on the t-shirts so that the total cost is $40? 3. 4x 136 You and four friends went to a ballet. Combined, you spent $136. What could tickets have cost? x + 6 A soccer team is on a 5 game tour. Their coach wants > 8 5 their scoring average to be 8 points. What must they score in the fifth game?

8 Puzzles, Twisters & Teasers Inequalities Scrambler The boxes below show the causes of certain changes to inequalities, and the effects on the inequalities. It is your task to match each cause with its effect and write them both beneath the two-step inequality they belong to. Each two-step inequality will have 2 causes and effects. Note that when multiplying or dividing an inequality by a negative number, the inequality must be reversed: x < 4 becomes x > 4 when divided by 1. Cause Effect add 2 to both sides 2x < 2 divide both sides by 2 x > 1 4 divide both sides by 3 3x > 15 subtract 2 from both sides multiply both sides by 4 x > 1 x > x 2 > 13 subtract 7 from both sides x > 5 2. x > x < 9

9 Answers LESSON Practice A 1. x < 3 2. x > 4 3. x 2 CODE at least 24 Practice C 1. x > 2 2. x 2 3. x > 6 4. x < 0 4.x 4 5. x 3 6. x < m ,000 Practice B 1. x 2 2. x 3 3. x > x 7 > 4; x > 1 x ; x no more than 150 Review for Mastery 1. x 2 2. x < 4 3. x > 7 4. x 1 4. x < 6 5. x 6 6. x < 4 Challenge 1. (1, 5), (1, 0), (2, 4) 2. (1, 5) 3. ( 4, 0), (6, 3) 4. y 20

10 5. Possible answer: (1, 11), (1, 10), (1, 9), (1, 8) 6. Possible answer: (2, 22), (2, 23), (2, 24), (2, 25) Problem Solving 1. at least 52 inches 2. no more than at least $1, B 5. G 6. D 7. J Reading Strategies 1. no less than or at least 2. at most or no more than 3. no more than 4. greater than Puzzles, Twisters & Teasers 1. add 2 to both sides: 3x < 15 divide both sides by 3: x > 5 2. subtract 2 from each side: x 4 > 1 multiply both sides by 4: x > 4 3. subtract 7 from both sides: 2x < 2 divide both sides by 2: x > 1