Solving Absolute Value Equations & Inequalities

Solving Absolute Value Equations & Inequalities Solving Absolute Value Equations & Inequalities Standard MM2A1c. Solve absolute value equations and inequalities analytically, graphically, and by using appropriate technology.

Absolute Value (of x) • Symbol lxl • The distance x is from 0 on the number line. • Always positive • Ex: l-3l=3 -4 -3 -2 -1 0 1 2

Ex: x = 5 • What are the possible values of x? x = 5 or x = -5

To solve an absolute value equation: ax+b = c, where c>0 To solve, set up 2 new equations, then solve each equation. ax+b = c or ax+b = -c ** make sure the absolute value is by itself before you split to solve.

Ex: Solve 6x-3 = 15 6x-3 = 15 or 6x-3 = -15 6x = 18 or 6x = -12 x = 3 or x = -2 * Plug in answers to check your solutions!

Ex: Solve 2x + 7 -3 = 8 Get the abs. value part by itself first! 2x+7 = 11 Now split into 2 parts. 2x+7 = 11 or 2x+7 = -11 2x = 4 or 2x = -18 x = 2 or x = -9 Check the solutions.

Your Turn: Solve 2x - 5 = 9

How do you solve absolute value inequalities? First, isolate the absolute value expression on the left side of the inequality Then choose the form of your inequality

Rewrite as ax+b < c And ax+b > -c, solve for x Rewrite as ax+b ≤ c And ax + b > -c, solve for x Rewrite as ax + b > c Or ax + b < -c, solve for x Rewrite as ax + b ≥ c Or ax + b ≤ -c, solve for x

Solve Solve

Ex: Solve & graph. • Becomes an “and” problem -3 7 8

Solve & graph. • Get absolute value by itself first. • Becomes an “or” problem -2 3 4

Your Turn: Solve & graph.

Homework:

Solving Absolute Value Equations & Inequalities