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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