Absolute value has two cases: the SAT math trap

Short answer: Split it: inside = +7 OR inside = −7. Absolute value almost always means two answers.

The trap, in one question

Tempting answer: 11  (only solved x − 4 = 7)

Correct answer: 8  (x = 11 or x = −3)

How to spot it in 3 seconds

Split it: inside = +7 OR inside = −7. Absolute value almost always means two answers.

FAQ

What is the absolute value has two cases trap on the SAT?

Example: What is the sum of all solutions to |x − 4| = 7? The tempting answer is 11 (only solved x − 4 = 7); the correct answer is 8 (x = 11 or x = −3).

How do you avoid the absolute value has two cases trap?

Split it: inside = +7 OR inside = −7. Absolute value almost always means two answers.

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