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Solving Equations with Absolute Values

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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

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.




x + 2 = 3 or x + 2 = –3

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




2x – 6 = 8 or 2x – 6 = –8

2x = 14 or 2x = –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.

Absolute Values On Both Side Of The Equation

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



3x + 3 = 2x + 5 or 3x + 3 = –(2x + 5)

Solving the first equation:

3x + 3 = 2x + 5

3x – 2x = 5 – 3

x = 2

Solving the second equation:

3x + 3 = –(2x + 5)

3x + 3 = –2x – 5

3x + 2x = –5 –3

5x = –8

How to solve equations if there is an absolute value expression on each side of the equation.

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