Solve for x

to determine if the equation has one, none, or infinite solutions.
3(2x+2)−4=−2x+10
(1 point)
Responses

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

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 one solution: x=0
.

1 answer

To solve for x, let's simplify the equation step by step:

3(2x+2) - 4 = -2x + 10

First, distribute the 3 to the terms inside the parentheses:

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

Combine like terms:

6x + 2 = -2x + 10

Next, move all the x terms to one side of the equation and the constant terms to the other side:

6x + 2x = 10 - 2

Combine like terms again:

8x = 8

Now, divide both sides of the equation by 8 to solve for x:

x = 1

Therefore, the equation has one solution: x = 1.