Question

Linear Expressions, Equations & Inequalities Unit Test
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Question
Which of the following equations has exactly one solution?(1 point)
Responses

−3x−8=3x−8
negative 3 x minus 8 equals 3 x minus 8

3x−8=3x+8
3 x minus 8 equals 3 x plus 8

−8x+3=−8x+3
negative 8 x plus 3 equals negative 8 x plus 3

−3x+8=−3x−8
negative 3 x plus 8 equals negative 3 x minus 8

Answer 1

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

1. **−3x − 8 = 3x − 8**
Rearranging, we get:
-3x - 3x = -8 + 8
-6x = 0
x = 0 (one solution)

2. **3x − 8 = 3x + 8**
Rearranging, we get:
3x - 3x = 8 + 8
0 = 16 (no solution)

3. **−8x + 3 = −8x + 3**
This equation simplifies to:
0 = 0 (infinitely many solutions)

4. **−3x + 8 = −3x − 8**
Rearranging, we get:
-3x + 3x = -8 - 8
0 = -16 (no solution)

Based on the analysis:
- The first equation has exactly one solution (x = 0).
- The second equation has no solution.
- The third equation has infinitely many solutions.
- The fourth equation has no solution.

Therefore, the equation **−3x − 8 = 3x − 8** has exactly one solution.