Solve for x

Question

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

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 no solution.
The equation has no solution.

The equation has one solution: x=10
.

Answer 1

To solve the equation \( 5(2x + 2) - 7x = 3x + 6 \), let's start by distributing and simplifying.

1. Distribute \( 5 \) on the left side: \[ 5(2x + 2) = 10x + 10 \]

2. Now, rewrite the equation: \[ 10x + 10 - 7x = 3x + 6 \]

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

4. Next, subtract \( 3x \) from both sides: \[ 10 = 6 \]

At this point, we end up with a false statement (\( 10 = 6 \)). This indicates that there are no values of \( x \) that satisfy the equation.

Thus, the equation has no solution.

The correct response is: The equation has no solution.