1. Solving Two-Step Inequalities
8.4
Solving Two-Step Inequalities
How do you solve a two-step inequality?

2. ADDITIONAL EXAMPLE 1
Use algebra tiles to model and solve 5f + 11 ≤ −4.
f ≤ −3

3. ADDITIONAL EXAMPLE 2
Ed wants to bicycle at least 75 miles this week. The inequality b ≥ 75 can be used to find b, the average number of miles he should bike on his
remaining 4 bike rides this week. Solve the inequality, and graph the solution set on a number line.
b ≥ 16

4. ADDITIONAL EXAMPLE 3
Dianna is buying lunch for herself and two friends. She has a coupon for $15 off the total bill and wants to spend less than $49 after using the coupon. The equation 3m − 15 < 49 can be
used to find m, the average price of each friend’s lunch. Determine which, if any, of the following values make the equation true: m = 21; m = 22; m = 23.
m = 21

5. 8.4 LESSON QUIZ 1. Solve − 10 ≤ 11. x ≤ 63 2. Solve 52 > −12 + 8d.
7.10.A, 7.11.A, 7.11.B 1.
Solve − 10 ≤ 11.
x ≤ 63 2.
Solve 52 > −12 + 8d.
d < 8 3.
Solve −16p ≥ −65.
p ≤ 11 4.
Charlene is a writer who is going on a trip. She has brought several copies of her latest book in her suitcase. The suitcase itself weighs 5 pounds, and each book weighs 3 pounds. If her full suitcase can weigh no more than 50 pounds, how many books can she bring?
at most 15 books

6. 5.
Carl is having a party. He has bought 24 brownies and is making 6 more batches of brownies. The inequality b ≥ 138 can be used to determine how many brownies, b, must be in each batch so that all 138 guests get at least 1 brownie. Determine which of the given values, if any, make the inequality true: b = 10; b = 15; b = 20.
b = 20

7. How do you solve a two-step inequality?
Sample answer:
Isolate the variable by performing the same operation on both sides of the inequality. If you divide both sides of the inequality by a negative number, reverse the inequality sign.