Question

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

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

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

Answer 1

Let's solve the equation step by step to determine how many solutions it has.

The given equation is:

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

First, distribute the 5 on the left side:

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

Now, simplify the left side:

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

Next, we will move the \(2x\) from the right side to the left side by subtracting \(2x\) from both sides:

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

This simplifies to:

\[ 8x + 6 = 6 \]

Now, subtract 6 from both sides:

\[ 8x = 0 \]

Finally, divide both sides by 8:

\[ x = 0 \]

Now, we find that we have one solution:

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