# Solving multi-step linear inequalities

### Solving multi-step linear inequalities

We learn how to solve multi-step linear inequalities in this lesson. Besides typical math questions, we are going to see word problems related to multi-step linear inequalities and money.

#### Lessons

• Introduction
i) What is an inequality?
ii) How to solve linear inequalities?
iii) How to graph inequalities on a number line?

• 1.
Solve.
a)
$10x - 25 = - 5x$

b)
$12.4 - 7.2x \le 10x - 15$

c)
$- \frac{3}{8} - 3x \le \frac{1}{8}x - 2$

d)
$\frac{1}{4}x + 2 \le - \frac{3}{4}\left( {3x - 5} \right)$

• 2.
Bob works for car dealer A which offers him a base rate of $800 and$15 for every car he sells. Tom works for car dealer B which gives him a base rate of $700 and$20 for each car he sells. If they sold the same number of cars last month, and Tom earned more than Bob. What is the minimum number of cars Tom sold last month?
a)
Express the problem in an inequality.

b)
Solve the inequality.

• 3.
The cost of a charity dinner is $300 plus$18 per guest. The ticket to the dinner is \$30 per person. How many tickets must be sold to cover the costs?