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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. 1.6 – Solve Linear Inequalities Example 1: a. Graph x < 2. b. Graph x > -1 1.6 – Solve Linear Inequalities Compound Inequalities: A compound inequality consists of two simple inequalities joined by “and” or “or”. 1.6 – Solve Linear Inequalities Example 2 a. Graph -1 < x < 2 b. Graph x < -2 or x > 1. 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. 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. 1.6 – Solve Linear Inequalities Example 4 Solve 5x + 2 > 7x – 4 1.6 – Solve Linear Inequalities Example 5 Solve -4 < 6x – 10 < 14 1.6 – Solve Linear Inequalities Example 6 Solve 3x + 5 < 11 or 5x – 7 > 23 .