2011 AMC 10A Problem 7

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.