Question

Determine if the equation has one solution, no solution, or infinite solutions.

2x + 2 = -2x + 10

Answer 1

To determine whether the equation \(2x + 2 = -2x + 10\) has one solution, no solution, or infinite solutions, we will solve it step by step.

1. Start with the original equation:
\[
2x + 2 = -2x + 10
\]

2. Add \(2x\) to both sides to eliminate \( -2x\) from the right side:
\[
2x + 2 + 2x = 10
\]
This simplifies to:
\[
4x + 2 = 10
\]

3. Now, subtract 2 from both sides to isolate the term with \(x\):
\[
4x + 2 - 2 = 10 - 2
\]
This simplifies to:
\[
4x = 8
\]

4. Finally, divide both sides by 4 to solve for \(x\):
\[
x = \frac{8}{4}
\]
Which simplifies to:
\[
x = 2
\]

Since we found a single value for \(x\), the equation \(2x + 2 = -2x + 10\) has **one solution**.