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 infinite solutions.
The equation has infinite solutions.

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

The equation has one solution: x=10.

Answer 1

To solve the equation \( 5(2x + 2) - 7x = 3x + 6 \), we will proceed step by step:

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

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

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

The equation \( 10 = 6 \) is a false statement, which indicates that there is no solution to the equation.

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