Question bank / Linear equations in one variable

Math · AlgebraMedium

How many solutions does the equation 3(2x−4)=6x−123(2x - 4) = 6x - 12 have?

A

Zero

B

Exactly one

C

Exactly two

D

Infinitely many

Show answer and explanation

Answer: D

Distribute the left side: 6x−126x - 12. The equation becomes 6x−12=6x−126x - 12 = 6x - 12, which is true for every value of xx. So the equation has infinitely many solutions.

Choice A is tempting because the xx-terms cancel, but the remaining statement −12=−12-12 = -12 is true, not false.

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