Solve for x

Question

to determine if the equation has one, none, or infinite solutions.
5(2x+2)−4=2x+6
(1 point)
Responses

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

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

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

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

Answer 1

Let's solve the equation step by step to determine how many solutions it has.

The given equation is:

$$5(2x+2)-4=2x+6$$

First, distribute the 5 on the left side:

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

Now, simplify the left side:

$$10x+6=2x+6$$

Next, we will move the $2x$ from the right side to the left side by subtracting $2x$ from both sides:

$$10x-2x+6=6$$

This simplifies to:

$$8x+6=6$$

Now, subtract 6 from both sides:

$$8x=0$$

Finally, divide both sides by 8:

$$x=0$$

Now, we find that we have one solution:

The equation has one solution: x equals 0.