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.
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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