Question

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 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.

The equation has one solution: x=0
.

Answer 1

Let's solve the equation step by step.

The equation is:

\[ 5(2x + 2) - 4 = 2x + 6 \]

First, distribute the 5 on the left side:

\[ 10x + 10 - 4 = 2x + 6 \]

This simplifies to:

\[ 10x + 6 = 2x + 6 \]

Now, subtract \(2x\) from both sides:

\[ 10x - 2x + 6 = 6 \]

Which simplifies to:

\[ 8x + 6 = 6 \]

Next, subtract 6 from both sides:

\[ 8x = 0 \]

Now, divide by 8:

\[ x = 0 \]

So, we found one solution, \(x = 0\).

### Conclusion:
The equation has **one solution: \( x = 0 \)**.