Absolute Value (of x) Symbol |x| The distance x is from 0 on the number line. Always positive Ex: |-3|=

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: Isolate the absolute value expression Remove the bars and write as two separate equations— one equal to positive, one equal to negative Solve each equation Check your answers 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 = 8 Get the abs. value part by itself first! 2x+7 = 11 Now split into 2 equations. 2x+7 = 11 or 2x+7 = -11 2x = 4 or 2x = -18 x = 2 or x = -9 Check the solutions.

Ex: Solve 2 4m + 10 = 12m Get the abs. value part by itself first! 4m+10 = 6m Now split into 2 equations. 4m+10 = 6m or 4m+10 = -6m 10 = 2m or 10 = -10m m = 5 or m = -1 Check the solutions. -1 is an extraneous solution

Homework: p.393 #3-30 multiples of 3