1.6 – Solve Linear Inequalities

1. 1.6 – Solve Linear Inequalities A linear inequality in one variable can be written in one of the following forms, where a and b are real numbers and a does not equal 0. A solution of an inequality in one variable is a value that, when substituted for the variable, results in a true statement. The graph of an inequality in one variable consists of all points on a number line that represent solutions.

2. 1.6 – Solve Linear Inequalities Example 1: Graph x < 2. Graph x > -1

3. 1.6 – Solve Linear Inequalities Compound Inequalities: A compound inequality consists of two simple inequalities joined by “and” or “or”.

4. 1.6 – Solve Linear Inequalities Example 2 Graph -1 < x < 2 Graph x < -2 or x > 1.

5. 1.6 – Solve Linear Inequalities Solving Inequalities: To solve a linear inequality in one variable, you isolate the variable using transformations that produce equivalent inequalities, which are inequalities that have the same solutions as the original inequality.

6. 1.6 – Solve Linear Inequalities Example 3 You have $50 to spend at a county fair. You spend $20 for admission. You want to play a game that costs $1.50. Describe the possible number of times you can play the game.

7. 1.6 – Solve Linear Inequalities Example 4 Solve 5x + 2 > 7x – 4

8. 1.6 – Solve Linear Inequalities Example 5 Solve -4 < 6x – 10 < 14

9. 1.6 – Solve Linear Inequalities Example 6 Solve 3x + 5 < 11 or 5x – 7 > 23 .