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 infinite solutions.
The equation has infinite solutions.

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

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

The equation has one solution: x=1
.
The equation has one solution: x equals 1 .
Remaining Attempts : 3
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Answer 1

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

1. Distribute on the left side:
\[
3(2x) + 3(2) - 4 = 6x + 6 - 4
\]
which simplifies to:
\[
6x + 2
\]

2. Now rewrite the equation:
\[
6x + 2 = -2x + 10
\]

3. Next, let's move all terms involving \( x \) to one side and constant terms to the other side. Start by adding \( 2x \) to both sides:
\[
6x + 2 + 2x = 10
\]
This simplifies to:
\[
8x + 2 = 10
\]

4. Now, subtract \( 2 \) from both sides:
\[
8x = 8
\]

5. Finally, divide both sides by \( 8 \):
\[
x = 1
\]

The solution is \( x = 1 \).

Now, we can check if this solution leads to one, none, or infinite solutions. Since we derived \( x = 1 \) and we arrived at a unique answer, this equation has **one solution: \( x = 1 \)**.

So the correct response is:

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