Question

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

The equation has one solution: x=1
.
The equation has one solution: x is equal to 1. - no response given

The equation has infinite solutions.
The equation has infinite solutions. - no response given

The equation has no solution.
The equation has no solution. - incorrect

The equation has one solution: x=0
.

Answer 1

Let's solve the equation step by step:

The equation is:

\[ 3(2x + 2) - 4 = -2x + 10 \]

1. **Distribute** on the left side:

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

2. **Combine like terms** on the left side:

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

3. **Add \( 2x \)** to both sides to get all \( x \) terms on one side:

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

This simplifies to:

\[ 8x + 2 = 10 \]

4. **Subtract 2** from both sides:

\[ 8x = 8 \]

5. **Divide by 8**:

\[ x = 1 \]

Now, let's determine the type of solution. Since we found a single value for \( x \) (which is \( x = 1 \)), the equation has **one solution**.

Thus, the correct response is:

The equation has one solution: x = 1.