Absolute Value & Radical Equations
Solve equations containing absolute values or square roots, split into cases and check for extraneous solutions. Try “solve |2x − 5| = 9”.
Try an example:
How the Absolute Value & Radical Equations works
- For |A| = k, solve the two cases A = k and A = −k.
- For a radical, isolate the root, then square both sides.
- Always substitute back: squaring can introduce extraneous solutions.
Frequently asked questions
What is an extraneous solution?
A value that satisfies the transformed equation but not the original one, so it must be discarded.
Can an absolute value equal a negative number?
No. |A| is never negative, so |A| = −3 has no solution.
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