Linear Inequalities Help

Introduction to Linear Inequalities

The solution to algebraic inequalities consists of a range (or ranges) of numbers. The solution to linear inequalities will be of the form x < a, x ≤ a, x > a , or x ≥ a , where a is a number. The inequality x < a means all numbers smaller than a but not including a; x ≤ a means all numbers smaller than a including a itself. Similarly the inequality x > a means all numbers larger than a but not a itself, and x≥a means all numbers larger than a including a itself.

The solutions to some algebra and calculus problems are inequalities. Sometimes you will be asked to shade these inequalities on the real number line and sometimes you will be asked to give your solution in interval notation. Every interval on the number line can be represented by an inequality and every inequality is represented by an interval on the number line. First we will represent inequalities by shaded regions on the number line. Later we will represent inequalities by intervals.

The inequality x < a is represented on the number line by shading to the left of the number a with an open dot at a .

A closed dot is used for x ≤ a .

Shade to the right of a for x > a.

• Use a closed dot for x ≥ a

Examples

Linear Inequalities Practice Problems

Practice

Shade the region on the number line.

1. x > 4

2. x > –5

3. x ≤1

4. x < –3

5. x ≥ 10

Solutions

Practice problems for this concept can be found at: Algebra Linear Inequalities Practice Test.