#### 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

**By:Kayla Blades**

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