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

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

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

The equation has one solution: x=1
.

1 answer

Let's solve the equation step by step.

The given equation is:

\[ 5(2x + 2) - 4 = 2x + 6 \]

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

\[ 10x + 10 - 4 = 2x + 6 \]

  1. Simplify the left-hand side:

\[ 10x + 6 = 2x + 6 \]

  1. Now, subtract \( 2x \) from both sides:

\[ 10x - 2x + 6 = 6 \]

This simplifies to:

\[ 8x + 6 = 6 \]

  1. Next, subtract \( 6 \) from both sides:

\[ 8x = 0 \]

  1. Finally, divide both sides by \( 8 \):

\[ x = 0 \]

Now that we have solved for \( x \), let’s analyze the solution:

The equation simplifies to \( x = 0 \), which means there is exactly one solution.

The correct response is:

The equation has one solution: x = 0.