Over Lesson 5–4

Solve the inequality. Show your work and 2 checks.

3t – 5 ≤ 13

Over Lesson 5–4

Solve the inequality

A. n 2.7

B. n 2.7

C. n 8.7

D. n 8.7

Over Lesson 5–4

A. r < 30

B. r < 3

C. r < –3

D. r < –30

Over Lesson 5–4

A. x –18

B. x –18

C. x 18

D. x 18

Over Lesson 5–4

A. t 6

B. t 6

C. t -6

D. t -6

Solve the inequality 3t – 5 ≤ 13.

You have already solved two-step equations and inequalities.

Solve multi-step inequalities.

Solve Equations and Inequalities with Parentheses

A. Solve (5x – 2)-3 ≥ 186. -3(5x + -2) ≥ 186 Write the

inequality. -3(5x) + -3(-2) ≥ 186

Distributive Property -15x + 6 ≥ 186 Simplify - 6 - 6 Subtract

6 from both sides -15x ≥ 180 Simplify. -15 -15 Divide by

-15 and reverse symbolAnswer: x ≤ -12

x ≤ -12

Simplify.

Solve Equations and Inequalities with Parentheses

A. Solve (5x – 2)-3 ≥ 186.

Answer: x ≤ 12

To check your solution, first check the solution and thentry any number less than -12.Check #1 (5x – 2)-3 = 186 Rewrite with an equal sign.

186 = 186 This statement is true.

-3(5(-20) – 2) ≥ 186 Replace x with -20 306 ≥ 186 This statement is true.

Check #2 (5x – 2)-3 ≥ 186 Write the inequality.

-3(5(-12) – 2) = 186 Replace x with -12.

Solve Equations and Inequalities with Parentheses

B. Solve 9(4k – 4) – 20k < 236. 9(4k + -4) + -20k < 236 Rewrite

the equation.9(4k) + 9(-4) + -20k < 236Distributive Property 36k + -36 + -20k < 236 Simplify. 16k + -36 < 236 Combine like terms. +36 +36 Add 36

to both sides

16k < 272 Simplify.

16 16Divide both sides by 16

k < 17 Simplify.

Solve Equations and Inequalities with Parentheses

B. Solve 9(4k – 4) – 20k < 236.

Answer: x < 17

To check your solution, first check the solution and thentry any number less than 17.Check #1 9(4k – 4) – 20k = 236 Rewrite with an equal sign.

236 = 236 This statement is true.

9(4(10) – 4) – 20(10) < 236 Replace k with 10 124 < 236 This statement is true.

Check #2 9(4k – 4) – 20k < 236 Write the inequality.

9(4(17) – 4) – 20(17) = 236 Replace k with 17.

A. Solve 4(x + 1) < 28.

B. Solve 35 ≥ 7(2p – 1).