Question

Solve for x to determine if the equation has one, none, or infinite solutions.
5(2x+2)−7x=3x+6 (1 point)
Responses

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

The equation has one solution: x=6.
The equation has one solution: x equals 6 .

The equation has one solution: x=10.
The equation has one solution: x equals 10 .

The equation has infinite solutions.

Answer 1

To solve the equation \( 5(2x + 2) - 7x = 3x + 6 \), we first simplify it step by step.

1. **Distribute the 5 on the left side:**
\[
5(2x) + 5(2) - 7x = 3x + 6
\]
\[
10x + 10 - 7x = 3x + 6
\]

2. **Combine like terms on the left side:**
\[
(10x - 7x) + 10 = 3x + 6
\]
\[
3x + 10 = 3x + 6
\]

3. **Subtract \(3x\) from both sides:**
\[
10 = 6
\]

At this point, we notice that \(10 = 6\) is a false statement. This indicates that the original equation has no solutions.

Therefore, the correct response is:
**The equation has no solution.**