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In this lesson we will be looking at solving equations with absolute values on one side of the equation and on both sides of the equation.

## Absolute Values On One Side Of The Equation

**Absolute Values On Both Side Of The Equation**

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

More Lessons for Algebra

Math Worksheets

In this lesson we will be looking at solving equations with absolute values on one side of the equation and on both sides of the equation.

When solving an equation with absolute values, it is necessary to split the equation into two equations, one resulting in a positive value and the other resulting in a negative value. We can then solve the two equations to obtain two possible solutions.

*Example: *

Solve

*Solution: *

*x* + 2 = 3 or *x* + 2 = –3

*x* = 1 or *x* = –5 (subtract 2 from both sides)

*Example: *

Solve

*Solution: *

2*x* – 6 = 8 or 2*x* – 6 = –8

2*x* = 14 or 2*x* = –2 (add 6 to both sides)

*x* = 7 or *x* = –1 (divide 2 to both sides)

The following video shows how to solve multi-step equations with absolute values.

The same method can be applied when there are absolute values on both side of the equation.

*Example: *

*Solution: *

3*x* + 3 = 2*x* + 5 or 3*x* + 3 = –(2*x* + 5)

**Solving the first equation: **

3*x* + 3 = 2*x* + 5

3*x* – 2*x* = 5 – 3

*x* = 2

**Solving the second equation:**

3*x* + 3 = –(2*x* + 5)

3*x* + 3 = –2*x* – 5

3*x* + 2*x* = –5 –3

5*x* = –8

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You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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