2011 AMC 10A Problem 7

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.

Problem 7 in other years