Question

Which of the following equations has infinitely many solutions? A. 2x + 5(2x + 6) = 12x + 30 B. 2x + 5 = 2 C. 2(x + 5) + 2 = 6x + 2(x + 2) D. 5x + 2 = 2x + 6

Answer 1

A. 2x + 5(2x + 6) = 12x + 30

Explanation:

Infinitely many solutions means the two sides of the equation will be equal to each other, so B and D can be eliminated. Distribute for A and C to check

A. 2x + 5(2x + 6) = 12x + 30

2x + 10x + 30 = 12x + 30

12x + 30 = 12x + 30

C. 2(x + 5) + 2 = 6x + 2(x + 2)

2x + 10 + 2 = 6x +2x + 4

2x + 12 = 8x + 4

You only get the same equation for A, therefore A is the correct answer