1. Inequalities Two-Step and Multi-Step Inequalities

2. Review Two-Step Inequalities 18 + 3t > -12

3. Review Two-Step Inequalities 7 ≤ 2t - 5

4. Multi-Step Inequalities How to Solve (Refresher): 1. Simplify each side of the inequality. (Distributive Property, Exponents, Combine Like Terms.) 2. Move the terms with variables to the left side of the inequality using inverse operations. 3. Move constants to the right side of the inequality using inverse operations. 4. Isolate the variable using inverse operations.

5. Multi-Step Inequalities 3 2 - 5 ≤ 2(1+x)

6. Multi-Step Inequalities 2(x+5) < 8

7. Multi-Step Inequalities y ≤ 6 + 4y

8. Multi-Step Inequalities -3(2-q) ≥ 6(q+1)

9. Multi-Step Inequalities x+5 ≥ x + 3 ● Does the same variable appear on both sides? ● Yes? Then look at the other terms. ● For any number x, will adding 5 always result in a greater number than when adding 3? ● What could be the solution? ● Let’s pick a number to substitute for x. What do we find? ● All values of x will make this inequality true. The solution is ALL REAL NUMBERS.

10. Multi-Step Inequalities 2(x+3) < 5 + 2x ● Does the same variable appear on both sides? ● Yes? Then look at the other terms. ● For any number 2x, will adding 6 ever result in a lesser number than when adding 5? ● Let’s pick a number to substitute for x. What do we find? ● No value of x will make this inequality true. There are NO SOLUTIONS.

11. Practice 1. b + 16 < 3b 2. 3(1 + k) > 4 +3k 3. 3t - 12 > 5t + 2 4. -3 (2r - 4) ≥ 2(5 - 3r)

12. Practice 1. b + 16 < 3b

13. Practice 2. 3(1 + k) > 4 +3k

14. Practice 3. 3t - 12 > 5t + 2

15. Practice 4. -3 (2r - 4) ≥ 2(5 - 3r)

16. School Orchestra a. The school orchestra is creating a CD of their last concert. The total cost is $400 plus $4.50 per CD. Write an expression for the cost of creating the CDs based on the number of CDs n.

17. School Orchestra b. The orchestra plans to sell the CDs for $12 each. Write an expression for the amount the orchestra earns from the sale of n CDs.

18. School Orchestra c. In order for the orchestra to make a profit, the amount they make selling the CDs must be greater than the cost of creating the CDs. Write an inequality that can be solved to find the number of CDs the orchestra must sell in order to make a profit. Solve your inequality.

19. Journal Write about the differences in solving multi-step equations and multi-step inequalities. Include a comparison of the solutions.

20. Homework P. 152 # 40-62 Even Test on Unit 3 Monday