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 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 \(5(2x + 2) - 7x = 3x + 6\), we'll start by expanding and simplifying both sides.

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

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

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

This statement \(10 = 6\) is a contradiction. Therefore, the original equation has no solutions.

So, the answer is: The equation has no solution.