Objective Students will be able to: write and solve multi-step inequalities, including real-world applications. CCM1: A-CED.1; A-REI.3 Designed by S.Tyler, HCPS Edited by L.Gilkey

How are inequality solutions different from equation solutions? Inequality solutions show the range of values that keep the inequality true. Equation solutions show THE value that keeps the equation true.

1) Solve 5m - 8 > 12 + 8 + 8 5m > 20 5 5 m > 4 + 8 + 8 5m > 20 5 5 m > 4 5(6) – 8 > 12 Draw “the river” Add 8 to both sides Simplify Divide both sides by 5 Check your answer Graph the solution o 4 5 3

2) Solve 12 - 3a > 18 - 12 - 12 -3a > 6 -3 -3 a < -2 - 12 - 12 -3a > 6 -3 -3 a < -2 12 - 3(-3) > 18 Draw “the river” Subtract 12 from both sides Simplify Divide both sides by -3 Simplify (Switch the inequality!) Check your answer Graph the solution o -2 -1 -3

Remember!! When using inverse operations, you FLIP the inequality sign when you MULTIPLY or DIVIDE by a NEGATIVE!!!

You Try! Which graph shows the solution to 2x - 10 ≥ 4? . Answer Now

3) Solve 5m - 4 < 2m + 11 o -2m -2m 3m - 4 < 11 + 4 + 4 + 4 + 4 3m < 15 3 3 m < 5 5(4) – 4 < 2(4) + 11 Draw “the river” Subtract 2m from both sides Simplify Add 4 to both sides Divide both sides by 3 Check your answer Graph the solution o 5 6 4

4) Solve 2r - 18 ≤ 5r + 3 ● -2r -2r -18 ≤ 3r + 3 - 3 - 3 -21 ≤ 3r 3 3 - 3 - 3 -21 ≤ 3r 3 3 -7 ≤ r or r ≥ -7 2(-7) – 18 ≤ 5(-7) + 3 Draw “the river” Subtract 2r from both sides Simplify Subtract 3 from both sides Divide both sides by 3 Check your answer Graph the solution ● -7 -6 -8

5) Solve -2x + 6 ≥ 3x - 4 x ≥ -2 x ≤ -2 x ≥ 2 x ≤ 2 Answer Now

6) Solve 26p - 20 > 14p + 64 o -14p -14p 12p – 20 > 64 + 20 + 20 + 20 + 20 12p > 84 12 12 p > 7 26(9) – 20 > 14(9) + 64 Draw “the river” Subtract 14p from both sides Simplify Add 20 to both sides Divide both sides by 12 Check your answer Graph the solution o 7 8 6

You Try: What are the values of x if 3(x + 4) - 5(x - 1) < 5? List three possible values for x _______, _______, & _______ Answer Now

7) Jason is building a deck for his sister at her new house 7) Jason is building a deck for his sister at her new house. Since she has a lot of land, she told him he could build it any size as long as it’s a rectangle and has a perimeter of at least 92 feet. What is the value of x so that the perimeter of the rectangle shown is at least 92 feet? 2 4+𝑥 +2(3𝑥)≥92 8+2𝑥+6𝑥≥92 8+8𝑥≥92 The value of x can be equal to or greater than 10.5 feet to build a deck with a perimeter of at least 92 feet. 8𝑥≥84 𝑥≥10.5

8) Ms. Salgado needs to have her car repaired but does not want to spend more than $225 for the repairs. The mechanic says that the part needed for the repair will cost $78, and that labor will cost an additional $35 per hour. Write and solve the inequality to represents the greatest number of hours the mechanic can work without exceeding Ms. Salgado’s budget? 78+35ℎ≤225 The mechanic can work on Ms. Salgado’s car for a maximum of 4.2 hours. 35ℎ≤147 ℎ≤4.2

9) The sum of a number and 8 is no more than -10. What is that number? 𝑛+8≤−10 The number has to be less than or equal to -18. 𝑛≤−18 10) Find three consecutive odd integers whose sum is at least 75. 𝑥+𝑥+2+𝑥+4≥75 The smallest combination of odd integers whose sum is at least 75 is 23, 25, 27. 3𝑥+6≥75 3𝑥≥69 𝑥≥23

11) Debbie has at most $60 to spend on clothes 11) Debbie has at most $60 to spend on clothes. She wants to buy a pair of jeans for $22 and spend the rest on t-shirts. If the cost of each shirt is $8, how many shirts can Debbie buy? 22+8𝑡≤60 Debbie can buy at most 4 shirts without going over her $60 limit. 8𝑡≤38 𝑡≤4.75