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# Absolute Value Equations and Inequalities

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on 27 October 2013

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#### Transcript of Absolute Value Equations and Inequalities

Equation 1

Equation 2

Inequality 1

Inequality 2
Absolute Value Equations and Inequalities
Absolute Value Inequality
Absolute Value of (2x-7)>11

Step 1: Isolate the absolute value.
|2x-7|>11
Step 2: Set up two inequalities since the sign is greater than then it is an or inequality.
2x-7>11 or 2x-7>-11
Step 3: Solve the inequalities.
2x-7>11 or 2x-7>-11
2x>18 or 2x>-4
x>9 or x>-2
Absolute value of (-5x-3)+2=7

Step 1: Write out the equation with the absolute value by itself.
|-5x-3|=5
Step 2: Set up two equations.
-5x-3=5 -5x-3=-5
Step 3: Solve both equations
-5x=8 -5x=-2
x=-8/5 x=2/5

Absolute Value Equation 1
Absolute Value Equation 2
Absolute value of (2x)-3=11

Step 1: Write out the equation with the absolute value by itself.
|2x|=14
Step 2: Set up two equations.
2x=14 2x=-14
Step 3: Solve both equations
2x/2=14/2 2x/2=-14/2
x=7 x=-7
Absolute Value Inequality 1
Absolute Value of (x-5)<4

Step 1: Isolate the value of the inequality.
|x-5|<4
Step 2: Set up your two inequalities as an And inequality because it is less than.
-4<x-5<4
Step 3: Solve the And inequality.
-4<x-5<4
-4+5<x-5+5<4+5
1<x<9
Graphs