16Hit1600
AlgebraVery hardConstant giving infinitely many solutions

Algebra practice question

In the equation 3(2x − c) = 6x − 15, c is a constant. For which value of c does the equation have infinitely many solutions?

  1. A. 5Correct
  2. B. −5
  3. C. 15
  4. D. No such value exists.

Answer: A. 5

Expand: 6x − 3c = 6x − 15. The x-terms match, so the equation holds for every x exactly when 3c = 15, c = 5.

Why the other answers are wrong

B. −5
c = −5 gives 6x + 15 = 6x − 15, never true.
C. 15
c = 15 gives 6x − 45 = 6x − 15, never true.
D. No such value exists.
c = 5 makes both sides identical.

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