2. Solving Linear Inequalities

The procedure for solving linear inequalities in one variable is similar to solving basic equations. (See Solving Equations.)

We need to be careful about the sense of the equality when multiplying or dividing by negative numbers.

Following are several examples of solving equations involving inequalities.

Example 1

Solve x + 2 < 4

Example 2

Solve `x/2>4`

Example 3

Solve 2x ≤ 4

Example 4

Solve the inequality 3 − 2x ≥ 15

Example 5

Solve the inequality `3/2(1-x)>1/4-x`

Inequalities with Three Members

Example 6

Solve −1 < 2x + 3 < 6

Example 7

Solve 2x < x − 4 ≤ 3x + 8

Exercises

Solve the following inequalities for x:

1. Solve 3 − 3x < − 1

2. Solve −2(x + 4) > 1 − 5x

3. Solve `x/5-2>2/3(x+3)`

4. Solve x − 1 < 2x + 2 < 3x + 1