AlgebraII Linear and Absolute Value Functions
Solving Linear Inequalities Concepts 1

|  |  | Definition |  |
. |
An inequality of the form where a and b are real numbers, is called a linear inequality in x. If the symbol < is replaced by >, the resulting inequality is also called a linear inequality.

Example 1. Solve 3·x + 5 < 0.

Solution

3·x + 5 < 0 | Write the inequality.
3·x < -5 | Add (-5).
| Divide by 3.
| Simplify fraction.

Answer: .

Example 2. Solve x - 5 > 3·x + 4.

Solution

x - 5 > 3·x + 4 | Write the inequality.
x - 5 + 5 > 3·x + 4 + 5 x > 3·x + 9 | Add 5.
x - 3·x > 3·x + 5 - 3·x -2·x > 9 | Add (-3·x).
| Divide by (-2). When both sides of an inequality are divided by a negative number, then the direction of the inequality is reversed.
| Simplify fraction.

Answer: .

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