1. Assignment Questions? Pg. 22-24 #24, 37, 40, 52, 58, 63 Pg. 30-31 #17, 22, 28, 33, 45*

2. Solving One-Variable, Compound and Absolute Value Inequalities Mr. Smith

3. Example 1 Solve 4y – 3 < 5y + 2. 4y – 3<5y + 2Original inequality 4y – 3 – 4y<5y + 2 – 4ySubtract 4y from each side. –3<y + 2Simplify. –3 – 2<y + 2 – 2Subtract 2 from each side. –5<ySimplify. y>–5Rewrite with y first.

4. Example 2 Original inequality Multiply each side by 2. Add –x to each side. Divide each side by –3, reversing the inequality symbol.

5. Solve the inequality 7 + 3y > 4(y + 2). A.{y | y > 1} B.{y | y < 1} C.{y | y > –1} D.{y | y < –1} Example 3

6. Example 4 CONSUMER COSTS Javier has at most $15.00 to spend today. He buys a bag of pretzels and a bottle of juice for $1.59. If gasoline at this store costs $2.89 per gallon, how many gallons of gasoline, to the nearest tenth of a gallon, can Javier buy for his car? UnderstandLet g = the number of gallons of gasoline that Javier buys. The total cost of the gasoline is 2.89g. The cost of the pretzels and juice plus the total cost of the gasoline must be less than or equal to $15.00.

7. Example 4 Original inequality Subtract 1.59 from each side. Simplify. The cost of pretzels & juice plus the cost of gasoline is less than or equal to $15.00. 1.59+2.89g  15.00 PlanWrite an inequality. Solve

8. Example 4 Divide each side by 2.89. Simplify. Answer: Javier can buy up to 4.6 gallons of gasoline for his car.

9. Example 5 “And” Compound Inequality Solve 10  3y – 2 < 19. Method 1Solve separately. Write the compound inequality using the word and. Then solve each inequality. 10  3y – 2and3y – 2 < 19 12  3y3y < 21 4  y y < 7 4  y < 7

10. Example 5 Solve an “And” Compound Inequality Method 2Solve both together. Solve both parts at the same time by adding 2 to each part. Then divide each part by 3. 10  3y – 2< 19 12  3y< 21 4  y< 7

11. Example 6 Solve x + 3 < 2 or –x  –4. Solve each inequality separately. –x  –4 or x + 3<2 x<–1 x4x4 Answer: The solution set is  x | x < –1 or x  4 . “Or” Compound Inequality

12. Concept

13. Example 7 Solve a Multi-Step Absolute Value Inequality Solve |2x – 2|  4. |2x – 2|  4 is equivalent to 2x – 2  4 or 2x – 2  –4. Solve each inequality. 2x – 2  4or2x – 2  –4 2x  62x  –2 x  3x  –1 Answer: The solution set is  x | x  –1 or x  3 .

14. Example 8 Solve a Multi-Step Absolute Value Inequality Solve |3x – 2| < 8.

15. Example 9 Write and Solve an Absolute Value Inequality A. JOB HUNTING To prepare for a job interview, Hinda researches the position’s requirements and pay. She discovers that the average starting salary for the position is $38,500, but her actual starting salary could differ from the average by as much as $2450. Write an absolute value inequality to describe this situation. Let x = the actual starting salary. Answer:|38,500 – x|  2450 The starting salary can differ from the average by as much as$2450. |38,500 – x|  2450

16. Example 9 Write and Solve an Absolute Value Inequality B. JOB HUNTING To prepare for a job interview, Hinda researches the position’s requirements and pay. She discovers that the average starting salary for the position is $38,500, but her actual starting salary could differ from the average by as much as $2450. Solve the inequality to find the range of Hinda’s starting salary. | 38,500 – x |  2450 Rewrite the absolute value inequality as a compound inequality. Then solve for x. –2450  38,500 – x  2450 –2450 – 38,500  –x  2450 – 38,500 –40,950  –x  –36,050 40,950  x  36,050

17. Example 9 Write and Solve an Absolute Value Inequality Answer: The solution set is  x | 36,050  x  40,950 . Hinda’s starting salary will fall within $36,050 and $40,950.

18. Assignment – Do Not Graph Pg. 37-38 #19, 20, 24, 36, 45 Pg. 45-47 #12, 14, 38, 41, 44(all but part ‘c’), 61