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Solve for x

to determine if the equation has one, none, or infinite solutions.
5(2x+2)−4=2x+6
(1 point)
Responses

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

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

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

The equation has one solution: x=0
.

1 answer

To solve the equation \( 5(2x + 2) - 4 = 2x + 6 \), we can start by simplifying both sides.

  1. Distribute on the left side: \[ 5(2x + 2) = 10x + 10 \] So the equation becomes: \[ 10x + 10 - 4 = 2x + 6 \] This simplifies to: \[ 10x + 6 = 2x + 6 \]

  2. Next, get all terms involving \( x \) on one side and constant terms on the other: \[ 10x - 2x = 6 - 6 \] This simplifies to: \[ 8x = 0 \]

  3. Now, solve for \( x \): \[ x = 0 \]

Since we found a specific value for \( x \), the equation has one solution: \( x = 0 \).

So the correct response is: The equation has one solution: x=0.