 # 1.7 Solving Absolute Value Equations & Inequalities

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1.7 Solving Absolute Value Equations & Inequalities
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Absolute Value (of x) Symbol lxl
The distance x is from 0 on the number line. Always positive Ex: l-3l=3

Ex: x = 5 What are the possible values of x? x = 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 = or 6x-3 = -15 6x = 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 = 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

Solve & graph. Get absolute value by itself first.
Becomes an “or” problem

Assignment