Question

Solve for x to determine if the equation has one, none, or infinite solutions. %0D%0A5(2x+2)−7x=3x+6(1 point)%0D%0AResponses%0D%0A%0D%0AThe equation has infinite solutions.%0D%0AThe equation has infinite solutions.%0D%0A%0D%0AThe equation has one solution: x=10.%0D%0AThe equation has one solution: x equals 10 .%0D%0A%0D%0AThe equation has one solution: x=6.%0D%0AThe equation has one solution: x equals 6 .%0D%0A%0D%0AThe equation has no solution.

Answer 1

To solve the equation, we will first distribute the 5 to the terms inside the parentheses:

5 * 2x + 5 * 2 - 7x = 3x + 6.

This simplifies to:

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

Next, we will combine like terms by subtracting 3x from both sides:

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

Simplifying further:

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

Now, combining like terms again:

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

Simplifying:

0 = -4.

Since we have obtained a contradiction (0 = -4 is not true), there are no solutions to this equation.

Therefore, the correct response is:

The equation has no solution.