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

5(2x+2)−4=2x+6(1 point)
Responses

The equation has infinite solutions.
The equation has infinite solutions.

The equation has one solution: x=1.
The equation has one solution: x equals 1 .

The equation has no solution.
The equation has no solution.

The equation has one solution: x=0.

1 answer

To solve for x, we first distribute the 5 on the left side of the equation: 10x + 10 - 4 = 2x + 6.
This simplifies to 10x + 6 = 2x + 6.
Next, we subtract 2x from both sides to eliminate x terms from one side of the equation: 8x + 6 = 6.
Then, subtract 6 from both sides to isolate the x term: 8x = 0.
Finally, divide by 8 to solve for x: x = 0.

Therefore, the equation has one solution: x=0.