Bell Ringer Solve for x: 2(𝑥−3) 3 = 𝑥 6

Solving Linear Inequalities 8/31/2017

Solving linear inequalities in one variable Multiply on both side by the least common denominator (LCD) to clear the inequality of fractions if they occur Use the distributive property to remove any parentheses if they occur Simplify each side of the inequality by combining like terms Write inequality with variable terms on one side and all numbers on the other side Get the variable alone

Most Important Rule When we multiply or divide by a negative the inequality symbol changes direction!!!!!!!!

Before we start… How do we graph an inequality? Use a number line to graph inequalities Graph: 𝑥≥6 𝑥<−3

Example 1 Solve and graph the inequality 𝑥+4≤−10

Example 2 Solve and graph the inequality −5𝑥+7<2(𝑥−3)

Example 3 Solve and graph the inequality 2 𝑥−3 −5≤3 𝑥+2 −18

Example 4 Compound Inequality Solve and graph the inequality 3≤ 3𝑥 2 +4≤5

Closing Task Write 3 things that are still confusing you about Linear Inequalities Write 2thing about linear inequalities that you understand Write 1 question about linear inequalities