Question

Which of the following equations has exactly one solution?(1 point)

3x−8=3x+8

−3x+8=−3x−8

−3x−8=3x−8

8 −8x+3=−8x+3

Answer 1

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

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

Simplifying:
\[
3x - 3x - 8 = 8 \implies -8 = 8
\]
This is a contradiction and has **no solution**.

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

Simplifying:
\[
-3x + 3x + 8 = -8 \implies 8 = -8
\]
This is also a contradiction and has **no solution**.

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

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

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

Simplifying:
\[
11 - 8x = -8x + 3 \implies 11 = 3
\]
This is also a contradiction and has **no solution**.

After analyzing all equations, we find that the third equation \(-3x - 8 = 3x - 8\) has exactly one solution.

**Answer: -3x - 8 = 3x - 8** (It has exactly one solution: \(x = 0\)).