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 4Solve the inequality and graph the solution. -2.5y > 3

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6.1 – Solving One-Step Linear Inequalities

HOMEWORK

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