Algebra practice question

Answer: A. k ≠ −15

Expand the left side: 6x − 15 = 6x + k. The 6x terms cancel, leaving −15 = k. If k = −15 the equation is true for EVERY x; for any other k it is never true, so there is no solution exactly when k ≠ −15.

Why the other answers are wrong

B. k = −15

k = −15 gives −15 = −15, which is always true — infinitely many solutions, not none.

C. k = 15

k = 15 is one of the many values that give no solution, but it isn't the condition that MUST hold.

D. k ≠ 15

k ≠ 15 allows k = −15, which gives infinitely many solutions rather than none.

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