# Absolute Value Equations

## Key Questions

• For example, $| x | = 0$ has only one solution $x = 0$.

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• Yes, it can; for example, $| x | = x$ has the solution set $\left[0 , \infty\right)$, which contains infinitely many solutions.

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• For absolute value, remember that the simplified version of the absolute value of a number will always be positive, because absolute value means the distance from 0. So that being said, the absolute value of |-78| is 78, because -78 is 78 places away from 0.

Once you know this, the rest is easy. Simplify all the absolute values, then solve normally. There will always be 2 answers, one positive one and one negative one. Make sure you list both on the test.

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