Radical & Absolute-Value Equations
Isolate the radical or the absolute value, then undo it, and always check.
The rules
- For a radical, isolate it, square both sides, solve, then check for extraneous solutions.
- For |expression| = k, solve expression = k and expression = −k.
- An absolute value can't equal a negative number.
- Check every answer in the original equation.
Watch out: Not checking, which leaves extraneous solutions.
Worked example
Solve |2x − 3| = 7.
- 2x − 3 = 7 gives x = 5.
- 2x − 3 = −7 gives x = −2.
Answer: x = 5 or x = −2
Try it yourself
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