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Published byAnis Mills Modified over 8 years ago

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**1.7 Solving Absolute Value Equations & Inequalities**

p. 50

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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

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

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**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.

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*** Plug in answers to check your solutions!**

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!

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**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.

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**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

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Ex: Solve & graph. Becomes an “and” problem

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**Solve & graph. Get absolute value by itself first.**

Becomes an “or” problem

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Assignment

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