7th Grade Math

Some inequalities involve more than one operation. To solve the

inequality, work backward to undo the operations, just as you did to

solve multi-step equations.

Solve a Multi-Step Inequality

Solve _^67 x + 15 > 9. Graph the solution set on a number line.

_ 76 x + 15 > 9 Write the inequality.

• 15 - 15 Subtract 15 from each side.

Step 1

Undo the

addition.

_^67 x > - 6 Simplify.

_^76 · _^67 x > _-^6

1

· _^76 Multiply each side by _^76.

Step 2

Undo the

multiplication.

x > - 7 Simplify.

Graph the solution, x > -7.

0 1 2 3 4 5 6 7 8 9 10 11

e. 3 x + 4 ≤ 31 f. 16 - 3 c > 14

Write an Inequality

JOBS Ling earns $8 per hour working at the zoo. Write and solve

an inequality that can be used to find how many hours she must

work in a week to earn at least $120.

Let x represent the number of hours worked.

Words

Variable

Inequality

Amount earned times number is at amount earned

per hour of hours least each week.

8 · x ≥ 120

8 · x ≥ 120

8 x ≥ 120

_^88 x ≥ _^1208 Divide each side by 8.

x ≥ 15 Simplify.

g. EARNINGS Elisa delivers pizzas. Her average tip is $1.50 for each

pizza that she delivers. Write and solve an inequality to

represent how many pizzas she must deliver to earn at least

$21 in tips.

Common Misconception Common Misconception

Do not reverse the

inequality sign just

because there is a

negative sign in the

inequality. Only reverse the

sign when you multiply or

divide each side by a

negative number.

Lesson 4C Inequalities 251

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