A student solved the following equation using the following steps:

2(2x + 2) = 4(x + 4)

4x + 4 = 4x + 4

4 = 4

Infinite solutions

Based on the student's work, the equation was solved ____ .

The equation solved correctly would show that it has _____ solution(s)

1 answer

The student's work is incorrect and does not solve the equation.

The equation has infinitely many solutions because both sides simplify to the same expression:

2(2x + 2) = 4(x + 4)

4x + 4 = 4x + 16

4x + 4x = 16 - 4

8x = 12

x = 3/2

Therefore, the equation has one solution.