2.7 Absolute Value Equations

Notes

The absolute value $|x|$ is a number's distance from 0, so it is never negative.

• $|x| = 5$ means $x = 5$ or $x = -5$.
• Isolate the absolute value first, then split: $|2x - 1| = 7 \Rightarrow 2x - 1 = 7$ or $2x - 1 = -7$, so $x = 4$ or $x = -3$.
• If an absolute value equals a negative number, there is no solution.