Every Candidate Is Guilty Until Checked

You'll learnto solve rational, radical, and absolute-value equations and check every candidate in the original.

Rational, radical, and absolute-value equations are quick to solve and easy to over-trust, because each one manufactures false candidates the algebra alone will not catch. Watch where the points leak — an extraneous solution reported without a check, a value that makes a denominator zero handed back as an answer, and only one case of an absolute value solved when there were two.

8 STEPS · 6 QUICK CHECKS · solve, then CHECK · two cases, or none · v3

candidates → check

Before you start

What you're looking at

A card naming three equation types — radical, rational, absolute-value — beside a panel showing one workflow: solve to candidates, then check.

The question

How can a value that solves cleanly still be false, and how do you catch it?

Watch for

Each type manufactures candidates that may not survive; watch the check in the original equation decide which ones are real.

What the symbols mean

The left card lists a sample equation per type; the right panel's flow runs given → solve → candidates → check → solutions.

The parts

Three equation families: 1 · Radical (and its check) → 2 · Rational → 3 · Absolute value — then a shared extraneous-candidate trap.

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