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=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. The equation has infinite solutions.

Answer 1

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

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

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

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

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

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