Question

Which of the following equations has exactly one solution
-8x+3=-8x+3
-3x-8=3x-8
-3x+8=-3x-8
3x-8=3x+8

Answer 1

To determine which of the given equations has exactly one solution, we need to analyze each equation.

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

This equation simplifies to \(0 = 0\), meaning it is true for all values of \(x\). Therefore, it has **infinitely many solutions**, not one.

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

Rearranging gives:
\[
-3x - 3x = -8 + 8
\]
\[
-6x = 0 \implies x = 0
\]
This equation has **exactly one solution**: \(x = 0\).

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

Rearranging gives:
\[
8 + 8 = -3x + 3x
\]
\[
16 = 0
\]
This is a contradiction, meaning there are **no solutions**.

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

Rearranging gives:
\[
3x - 3x = 8 + 8
\]
\[
0 = 16
\]
This is also a contradiction, meaning there are **no solutions**.

In conclusion, the equation that has exactly one solution is:

**-3x - 8 = 3x - 8** with the solution \(x = 0\).