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 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 . The equation has one solution: x equals 10 . The equation has infinite solutions.

Answer 1

To determine the number of solutions for the equation \(5(2x+2)−7x=3x+6\), we first simplify it.

1. Start with the original equation: \[ 5(2x + 2) - 7x = 3x + 6 \]

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

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

4. To isolate the variable, subtract \(3x\) from both sides: \[ 10 = 6 \]

This statement is false, indicating that the equation does not hold for any value of \(x\).

Therefore, the equation has no solution.

The correct response is: The equation has no solution.