Question

Which equation has infinitely many solutions?

A. -5(x + 2) = -4x − 12 − x + 2


B. 3x − 4 + 2x = 5(x − 4)


C. 5(x + 7) = -5(x − 7)


D. 6x + 2 − x = -2x − 2 + 7x

Answer 1

9514 1404 393

Answer:

A

Explanation:

We can eliminate parentheses, collect terms, and subtract the right-side expression from both sides to put these equations in general form. Then it is very easy to tell how many solutions there are .

A. -5x -10 = -5x -10

0 = 0 . . . . . true for all values of x; infinite solutions

B. 5x -4 = 5x -20

16 = 0 . . . . . not true for any value of x; no solutions

C. 5x +35 = -5x +35

10x = 0 . . . . . true for x=0; one solution

D. 5x +2 = 5x -2

4 = 0 . . . . . not true for any value of x; no solutions