Solve for x to determine if the equation has one, none, or infinite solutions.

5(2x+2)−7x=3x+6

A. The equation has no solution.

B. The equation has infinite solutions.

C. The equation has one solution: x=6.

D. The equation has one solution: x=10

1 answer

To solve for x, we can start by simplifying the equation by multiplying the numbers outside the parentheses:

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

Next, we can combine like terms by moving the variables to one side of the equation and the constants to the other side:

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

-3x = -4

Now, we can solve for x by dividing both sides of the equation by -3:

x = (-4)/(-3)

x = 4/3

Since x is not a whole number, the equation has no solution.

Therefore, the correct answer is:

A. The equation has no solution.