Solve for x to determine if the equation has one, none, or infinite solutions.

Question

5(2x+2)−4=2x+6
A. The equation has one solution: x=1.
B. The equation has no solution.
C. The equation has infinite solutions.
D. The equation has one solution: x=0.

Answer 1

D. The equation has one solution: x=0.

To solve for this, we first distribute the 5 on the left side:
10x + 10 - 4 = 2x + 6
Combine like terms:
10x + 6 = 2x + 6
Subtract 2x from both sides:
8x + 6 = 6
Subtract 6 from both sides:
8x = 0
Divide by 8:
x = 0

Therefore, x=0 is the solution to the equation.