Solving Absolute Value Equations & Inequalities

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.

* Plug in answers to check your solutions! 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!

Get the abs. value part by itself first! 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.

Solving Absolute Value Inequalities ax+b < c, where c>0 Becomes an “and” problem Changes to: –c<ax+b<c ax+b > c, where c>0 Becomes an “or” problem Changes to: ax+b>c or ax+b<-c

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