SYNTENE LEARN . SAT MATH . ALGEBRA
How many distinct real solutions does |x - 5| = 2x - 4 have?
Answer: B) Exactly one. Cases give x = -1 (extraneous: 6 \ne -6) and x = 3 (valid). Exactly one.
Step-by-step solution
Cases give x = -1 (extraneous: 6 \ne -6) and x = 3 (valid). Exactly one.
Common mistake
Counting both cases without checking. Absolute-value equations hide extraneous roots.
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What is the answer to How many distinct real solutions does |x - 5| = 2x - 4 have?
Answer: B) Exactly one. Cases give x = -1 (extraneous: 6 \ne -6) and x = 3 (valid). Exactly one.
How do you solve it?
Cases give x = -1 (extraneous: 6 \ne -6) and x = 3 (valid). Exactly one.
What mistake do most students make?
Counting both cases without checking. Absolute-value equations hide extraneous roots.
What SAT topic is this?
Algebra. Practice more free Algebra questions with instant feedback at Syntene Learn.