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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 - PowerPoint PPT Presentation

Solving Absolute Value Equations & InequalitiesSolving Absolute Value Equations & InequalitiesMM2A1c. Solve absolute value equations and inequalities analytically, graphically, and by using appropriate technology.

Absolute Value (of x)Symbol lxlThe distance x is from 0 on the number line.Always positiveEx: l-3l=3 -4 -3 -2 -1 0 1 2

Ex: x = 5What 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 = 156x-3 = 15 or 6x-3 = -156x = 18 or 6x = -12x = 3 or x = -2

* Plug in answers to check your solutions!

Ex: Solve 2x + 7 -3 = 8Get the abs. value part by itself first!2x+7 = 11Now split into 2 parts.2x+7 = 11 or 2x+7 = -112x = 4 or 2x = -18x = 2 or x = -9Check 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 inequalityThen choose the form of your inequality

Rewrite as ax+b < cAnd ax+b > -c,solve for xRewrite asax+b c Andax + b > -c, solve for xRewrite asax + b > cOrax + b < -c,solve for xRewrite asax + b cOrax + 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: