Question

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

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

The equation has one solution: x = 6

The equation has infinite solutions.

The equation has one solution: x = 10

The equation has no solution.

Answer 1

To solve the given equation, we simplify both sides:

5(2x + 2) - 7x = 3x + 6
10x + 10 - 7x = 3x + 6
3x + 10 = 3x + 6

We notice that there is a 3x term on both sides of the equation. Subtracting 3x from both sides gives us:

10 = 6

This is clearly not true. Therefore, the equation has no solution. The correct answer is:

The equation has no solution.