Given the function f(x) = –0.5|2x + 2| + 1, for what values of x is f(x) = 6?

Because an absolute value is always nonnegative, |2x + 2| ≥ 0. Multiplying it by −0.5 gives a value that is at most 0, so f(x) = −0.5|2x + 2| + 1 can never be greater than 1. Therefore it cannot equal 6, and the correct choice is “no solution.”

AI-written and checked against the verified answer.