Question

Which of the following equations does not have a solution?

$(x + 7)^2 = 0$

$|-3x| + 5 = 0$

$\sqrt{-x} - 2 = 0$

$\sqrt{x} - 8 = 0$

$|-3x| - 4 = 0$

Check which equation asks a nonnegative expression to be negative

An absolute value plus $5$ cannot equal $0$

A simplifies to $x + 7 = 0$ $x = -7,$ so it has a solution.

B simplifies to $|-3x| = -5,$ which has no solution since absolute value makes everything positive.

Let us make sure that all the other choices have solutions.

C simplifies to $\sqrt{-x} = 2$ $-x = 4$ $x = -4,$ which is fine.

D simplifies to $\sqrt{x} = 8$ $x = 64,$ which works.

Finally, E simplifies to $|-3x| = 4$ $-3x = \pm 4$ $x = \pm \dfrac{4}{3},$ which has a solution as well.

Thus, B is the correct answer.