# 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 2*x* ≤ 4

### Example 4

Solve the inequality 3 − 2*x* ≥ 15

### Example 5

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

Continues below ⇩

## Inequalities with Three Members

### Example 6

Solve −1 < 2*x* + 3 < 6

### Example 7

Solve 2*x *<* x* − 4 ≤ 3*x* + 8

### Exercises

Solve the following inequalities for *x*:

1. Solve 3 − 3*x* < − 1

2. Solve −2(*x* + 4) > 1 − 5*x*

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

4. Solve *x* − 1 < 2*x* + 2 < 3*x* +
1

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