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Solve for x

to determine if the equation has one, none, or infinite solutions.
5(2x+2)−7x=3x+6
(1 point)
Responses

The equation has infinite solutions.
The equation has infinite solutions.

The equation has one solution: x=10
.
The equation has one solution: x equals 10 .

The equation has no solution.
The equation has no solution.

The equation has one solution: x=6
.

1 answer

To solve the equation \( 5(2x + 2) - 7x = 3x + 6 \), let's first simplify the left side of the equation.

  1. Distribute \( 5 \) on the left side:

\[ 5(2x) + 5(2) - 7x = 10x + 10 - 7x \]

This simplifies to:

\[ (10x - 7x + 10) = 3x + 6 \]

  1. Combine like terms:

\[ 3x + 10 = 3x + 6 \]

  1. Subtract \( 3x \) from both sides:

\[ 10 = 6 \]

This statement is false. Since we reached a contradiction, this means that there are no values of \( x \) that satisfy the equation.

Therefore, the correct response is:

The equation has no solution.