Question

Which of the following equations has exactly one solution?
1. -8x+3=-8x+3
2. 3x-8=3x-8
3.-3x+8=3x-8
4. -3x +8=-3x-8

Answer 1

To determine which of the given equations has exactly one solution, we can analyze each equation:

1. **Equation: -8x + 3 = -8x + 3**

This equation simplifies to 0 = 0, which is true for all values of \( x \). Therefore, it has infinitely many solutions.

2. **Equation: 3x - 8 = 3x - 8**

Similar to the first equation, this simplifies to 0 = 0, which is also true for all values of \( x \). Thus, it has infinitely many solutions.

3. **Equation: -3x + 8 = 3x - 8**

To solve for \( x \):
\[
-3x + 8 = 3x - 8
\]
Combine like terms:
\[
8 + 8 = 3x + 3x
\]
\[
16 = 6x
\]
Divide by 6:
\[
x = \frac{16}{6} = \frac{8}{3}
\]
This equation has exactly one solution: \( x = \frac{8}{3} \).

4. **Equation: -3x + 8 = -3x - 8**

To solve for \( x \):
\[
-3x + 8 = -3x - 8
\]
Add \( 3x \) to both sides:
\[
8 = -8
\]
This is a contradiction, which means there are no solutions.

**Conclusion:**
The only equation from the list that has exactly one solution is **3. -3x + 8 = 3x - 8**.