Solve for x to determine if the equation has one, none, or infinite solutions.

Question

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

Let's solve the equation step-by-step:

Given: \[ 5(2x + 2) - 7x = 3x + 6 \]

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

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

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

This statement is false. Since we reached a contradiction, the equation has no solution.

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