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 no solution.
The equation has no solution.

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.

Answer 1

To solve the equation \(5(2x+2)−4=2x+6\), let's first simplify the left side:

1. Distribute the 5: \[ 5(2x) + 5(2) - 4 = 10x + 10 - 4 \] This simplifies to: \[ 10x + 6 \]

2. Now, rewrite the equation: \[ 10x + 6 = 2x + 6 \]

3. Next, we'll isolate \(x\) by subtracting \(2x\) and \(6\) from both sides: \[ 10x - 2x + 6 - 6 = 2x - 2x + 6 - 6 \] This gives us: \[ 8x = 0 \]

4. Now, divide both sides by 8: \[ x = 0 \]

Since we found a solution for \(x\), we have one solution.

Thus, the correct response is: The equation has one solution: x equals 0.