Question

Solve for x to determine if the equation has one, none, or infinite solutions.
3(2x+2) -4=-2x +10
(1 point)
The equation has one solution:
• x = 1.
• The equation has no solution.
• The equation has infinite
solutions.
The equation has one solution:
x = 0.

Answer 1

Let's solve the equation step by step to determine the solution for \( x \):

Given equation:

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

First, distribute \( 3 \) to the terms inside the parentheses on the left side:

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

Now simplify the left side:

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

Next, add \( 2x \) to both sides to get all the \( x \) terms on one side:

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

This simplifies to:

\[ 8x + 2 = 10 \]

Next, subtract \( 2 \) from both sides:

\[ 8x = 8 \]

Now, divide both sides by \( 8 \):

\[ x = 1 \]

### Conclusion

The equation has **one solution**, which is:

\[ x = 1 \]

Thus, the correct option is: **The equation has one solution: x = 1.**