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

Question

5(2x + 2) - 7x = 3x + 6 (1 point)

The equation has infinite solutions.
The equation has no solution.
The equation has one solution: x = 6
The equation has one solution: x = 10

Answer 1

To solve the equation, first distribute the 5 on the left side:

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

Combine like terms:

3x + 10 = 3x + 6

Subtract 3x from both sides:

10 = 6

Since the resulting statement is false (10 is not equal to 6), the equation has no solution. Therefore, the correct answer is:

The equation has no solution.