Solving Linear Inequalities

To solve linear inequalities, we find the values of the variable that make the inequality true. The process is similar to solving linear equations, but we must consider the direction of the inequality sign when multiplying or dividing by negative numbers.

Example Problem

Solve the inequality: $-3x + 5 < 11$

Step 1: Subtract 5 from both sides. $-3x < 11 - 5$
$-3x < 6$

Step 2: Divide both sides by -3. Remember to reverse the inequality sign. $x > \frac{6}{-3}$ $x > -2$

Solution

The solution to the inequality is:
$x > -2$

Key Questions

• What happens to the inequality sign when multiplying by a negative number?
• How would you graph the solution of the inequality $x < 4$?
• Solve the inequality $2x - 3 \geq 5$ and state the solution set.
• What is the solution to the compound inequality $-1 < 2x + 3 < 5$?

Keywords

• Inequality
• Solution
• Graphing
• Compound Inequality
• Reversal of Inequality Sign