Solving Inequalities with Variables on Both Sides

Transcription

1 Warm Up Lesson Presentation Lesson Quiz 1 Section 3-5 1

2 2 pts Bell Quiz 3-5 Solve each equation. 1. 2x = 7x pts 2. Solve and graph 5(2 b) > pts possible Section 3-5 2

3 Questions on 3-4 Section 3-5 3

4 Objective Solve inequalities that contain variable terms on both sides. Section 3-5 4

5 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. Section 3-5 5

6 3 STEPS TO SOLVING 1. SimPlify = PEMDAS (LHS/RHS) 2. Collect variables 3. Solve = SADMEP Section 3-5 6

7 Example 1A: Variables on Both Sides Solve the inequality and graph the solutions. y 4y + 18 To collect the variable terms on one side, subtract y from both sides. 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. Section 3-5 7

8 Example 1B: Variables on Both Sides Solve the inequality and graph the solutions. 4m 3 < 2m + 6 To collect the variable terms on one side, subtract 2m from both sides. Since 3 is subtracted from 2m, add 3 to both sides to undo the subtraction Since m is multiplied by 2, divide both sides by 2 to undo the multiplication. Section 3-5 8

9 Check It Out! Example 1 Solve the inequality and graph the solutions. 1a: 4x 7x - 6 1b: 5t + 1 < 2t 6 Section 3-5 9

10 Skip Example 2 Section

11 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. Section

12 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 the inequality. 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. Section

13 Example 3B: Simplify Each Side Before Solving Solve the inequality and graph the solution. 0.9y 0.4y 0.5 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. Section

14 Check It Out! Example 3 Solve the inequality and graph the solutions. 3a: 5(2 r) 3(r 2) 3b: 0.5x x < 0.3x + 6 Section

15 There are special cases of inequalities called identities and contradictions. Section

16 Section

17 Example 4A: Identities and Contradictions Solve the inequality. 2x x Subtract 2x from both sides. The inequality 2x x is an identity. All values of x make the inequality true. Therefore, all real numbers are solutions. 17

18 Example 4B: Identities and Contradictions Solve the inequality. 2(3y 2) 4 3(2y + 7) Distribute 2 on the left side and 3 on the right side. Subtract 6y from both sides. No values of y make the inequality true. There are no solutions. 18

19 Check It Out! Example 4 Solve the inequality. 4a: 4(y 1) 4y + 2 4b: x 2 < x + 1 Section

20 HOMEWORK Sec 3-5: (Pg 197) 3, 7, 10, 14, 15, 21, 24, 25, 28, 30, 31, 34, 36, 37, 41, 43, 44, 52, 53 (14, 15, 36, 37, 52, 53 DO NOT need graphs; all other problems DO need graphs. Graphs are due in 2 class periods on paper. Still type inequality answers in online.) Section