 # Chapter 6 – Solving and Graphing Linear Inequalities

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Chapter 6 – Solving and Graphing Linear Inequalities
6.1 – Solving One-Step Linear Inequalities

6.1 – Solving One-Step Linear Inequalities
Today we will learn how to: Graph linear inequalities in one variable Solve one-step linear inequalities

6.1 – Solving One-Step Linear Inequalities
The GRAPH of a linear inequality in one variable is the set of points on a number line that represent all solutions of the inequality.

6.1 – Solving One-Step Linear Inequalities
Verbal Phrase All real numbers less than 2 All real numbers greater than -2 All real numbers less than or equal to 1 All real numbers greater than or equal to 0 Inequality x < 2 x > -2 x ≤ 1 x ≥ 0

6.1 – Solving One-Step Linear Inequalities
An open dot is used for < and > A closed dot is used for ≤ and ≥

6.1 – Solving One-Step Linear Inequalities
Example 1 Abu was sure he didn’t score less than a 73 on his algebra test. Write and graph an inequality to describe Abu’s possible score.

6.1 – Solving One-Step Linear Inequalities
Solving a linear inequality in one variable is much like solving a linear equation in one variable. To solve the inequality, you get the variable on one side using inverse operations.

6.1 – Solving One-Step Linear Inequalities
Transformations that produce equivalent inequalities Add the same number to each side x – 3 < 5 Subtract the same number from each side x + 6 ≥ 10

6.1 – Solving One-Step Linear Inequalities
Example 2 Solve x + 8 ≥ 1. Graph the solution.

6.1 – Solving One-Step Linear Inequalities
Example 3 Solve 3 < m – 5. Graph the solution.

6.1 – Solving One-Step Linear Inequalities
USING MULTIPLICATION AND DIVISION The operations used to solve linear inequalities are similar to those used to solve linear equations, but there are important differences. When you multiply or divide each side of an inequality by a negative number, you must reverse the inequality symbol to maintain a true statement. For instance, to reverse >, replace it with <.

6.1 – Solving One-Step Linear Inequalities
Transformations that produce equivalent inequalities Multiply each side by the same positive number ½ x > 3 Divide each side by the same positive number 3x ≤ 9

6.1 – Solving One-Step Linear Inequalities
Transformations that produce equivalent inequalities Multiply each side by the same negative number and reverse the sign -x < 4 Divide each side by the same negative number and reverse the sign -2x ≤ 6

6.1 – Solving One-Step Linear Inequalities
Example 4 Solve the inequality and graph the solution. -2.5y > 3

6.1 – Solving One-Step Linear Inequalities
HOMEWORK Page 337 #22 – 54 even