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 no solution.
.
The equation has one solution: x=6.

The equation has one solution: x=10.

The equation has infinite solutions.

Answer 1

To solve the equation, we will simplify and combine like terms:

5(2x+2) - 7x = 3x + 6

First, distribute the 5 on the left side:

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

Combine like terms:

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

Simplify further:

3x + 10 = 3x + 6

Since the variable x appears on both sides of the equation and the coefficients are the same, we can subtract 3x from both sides:

10 = 6

This equation is not true regardless of the value of x. Therefore, the equation has no solution.