Solve for x to determine if the equation has one, none, or infinite solutions. 5(2x+2)−7x=3x+6 (1 point)ResponsesThe equation has no solution.The equation has no solution.The equation has one solution: x=10.The equation has one solution: x equals 10 .The equation has one solution: x=6.The equation has one solution: x equals 6 .The equation has infinite solutions.

Answer 1

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

1. Distribute \(5\) 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: \[ (10x - 7x) + 10 = 3x + 6 \] This simplifies to: \[ 3x + 10 = 3x + 6 \]

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

This outcome is a contradiction, meaning there are no values of \(x\) that will satisfy the equation. Therefore, the equation has no solution.

The final answer is: The equation has no solution.