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Solve for x

to determine if the equation has one, none, or infinite solutions.
3(2x+2)−10x=−4x+6
(1 point)
Responses

The equation has one solution: x=−1
.
The equation has one solution: x equals negative 1 .

The equation has one solution: x=0
.
The equation has one solution: x equals 0 .

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

The equation has no solution.

1 answer

To solve the equation \( 3(2x + 2) - 10x = -4x + 6 \), let's start by simplifying both sides.

  1. Distribute on the left side:

\[ 3(2x + 2) = 6x + 6 \]

So the equation becomes:

\[ 6x + 6 - 10x = -4x + 6 \]

  1. Combine like terms on the left side:

\[ (6x - 10x) + 6 = -4x + 6 \] \[ -4x + 6 = -4x + 6 \]

  1. Now, we have:

\[ -4x + 6 = -4x + 6 \]

This indicates that both sides of the equation are identical. This means that this equation is true for all values of \( x \).

Therefore, the equation has infinite solutions.

The correct response is:

The equation has infinite solutions.