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 one solution: x=10.
The equation has one solution: x equals 10 .

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.

Answer 1

To solve the equation, let's simplify both sides:

5(2x+2)−7x=3x+6

10x + 10 - 7x = 3x + 6

(10x - 7x - 3x) + (10 - 6) = 0

0 = 0

Since both sides of the equation are equal to 0, this means that the equation has infinite solutions.