|u| = 5 means u is 5 units from zero in either direction, so u = 5 or u = −5. Every absolute-value equation splits into those two cases; solve each and keep the solutions consistent with the case they came from.
Worked example: |x - 2| = 5
Step by step
- \left|{x - 2}\right| = 5
Start from the equation as given.
- \left|{x - 2}\right| - 5 = 0
Split into the two cases inside the absolute value: positive and negative.
- x - 7 = 0 \Rightarrow x = 7
Case x - 2 non-negative: replace |x - 2| by (x - 2) and solve; keep only solutions consistent with that case.
- - x - 3 = 0 \Rightarrow x = -3
Case x - 2 negative: replace |x - 2| by −(x - 2) and solve; keep only solutions consistent with that case.
Reveal the answer
x = 7 ,\; x = -3
Try your own
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