Question

Which of the following equations has exactly one solution? (1 point)
-3x + 8 = -3x - 8

-3x - 8 = 3x - 8

3x - 8 = 3x + 8

-8x + 3 = -8x + 3

Answer 1

To determine which of the given equations has exactly one solution, we will solve each equation step-by-step.

1. **Equation 1:** \(-3x + 8 = -3x - 8\)

By adding \(3x\) to both sides:
\[
8 = -8
\]
This is a false statement. Therefore, there are no solutions.

2. **Equation 2:** \(-3x - 8 = 3x - 8\)

By adding \(3x\) to both sides:
\[
-8 = 6x - 8
\]
Adding 8 to both sides:
\[
0 = 6x
\]
Dividing by 6:
\[
x = 0
\]
This equation has exactly one solution: \(x = 0\).

3. **Equation 3:** \(3x - 8 = 3x + 8\)

By subtracting \(3x\) from both sides:
\[
-8 = 8
\]
This is a false statement. Therefore, there are no solutions.

4. **Equation 4:** \(-8x + 3 = -8x + 3\)

Both sides are the same, which means:
\[
0 = 0
\]
This is true for all \(x\). Therefore, there are infinitely many solutions.

From the above analysis, **the equation that has exactly one solution is the second one:**
\[
-3x - 8 = 3x - 8
\]