Chapter Contents

• Inequalities
• 1. Properties of Inequalities
• 2. Solving Linear Inequalities
• 3. Solving Non-Linear Inequalties
• 4. Inequalities Involving Absolute Values
• Inequalities Problem Solver

• Comments, Questions?

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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

Answer

Example 2

Solve `x/2>4`

Answer

Example 3

Solve 2x ≤ 4

Answer

Example 4

Solve the inequality 3 − 2x ≥ 15

Answer

Example 5

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

Answer

Inequalities with Three Members

Example 1

Solve − 1 < 2x + 3 < 6

Answer

Example 2

Solve 2x < x − 4 ≤ 3x + 8

Answer

Exercises

Solve the following inequalities

1. Solve 3 - 3x < − 1

Answer

2. Solve -2(x + 4) > 1 − 5x

Answer

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

Answer

4. Solve x − 1 < 2x + 2 < 3x + 1

Answer