Solve for x

Question

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.