Solving Multistep Inequalities

Honors Math – Grade 8

Get Ready for the LessonSally wants to cater a party, but she needs to spend less than $800. If the caterer charges $350 to set up the event and $12.50 per person, how many guests can Sally invite?

Write and solve an inequality. Cost per

person+ Set-up

Fee < 800

12.50𝑔+350<800Define a variable.

A Multistep Inequality is an inequality containing more than one mathematical operation.

A multistep inequality is solved the same way a multistep equation is solved.

Solve each inequality. Then graph the solution.

9 𝑦+12<−12

Solve each inequality. Then graph the solution.

15>−2𝑚−5

Solve each inequality. Then graph the solution.

23 +14 𝑐≥

34

Solve each inequality. Then graph the solution.

5+10 ≥ 15 𝑐+20− 25 𝑐

Solve each inequality. Then graph the solution.

10≤−7−4 h−2

Solve each inequality. Then graph the solution.

3 (2 𝑦+1 )−2≤31

Solve each inequality. Then graph the solution.

2 (𝑑+5 )+8𝑑 ≥4

Solve each inequality. Then graph the solution.

3 𝑥− (7 𝑥−11)>9

Solve each inequality. Then graph the solution.

4 (−2𝑛+8 )>−16

Solve each inequality. Then graph the solution.

− 𝑥3 +14 ≤

16

Solve each inequality. Then graph the solution.

−0.3+4.4h<5.2

Solve each inequality. Then graph the solution.

1−0.4𝑟 ≤3.4−0.6𝑟