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
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 minus 8 equals 3 x minus 8

−3x+8=−3x−8

Answer 1

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

1. **3x - 8 = 3x + 8**:
Subtracting \(3x\) from both sides gives \(-8 = 8\), which is a false statement. Therefore, this equation has no solution.

2. **−8x + 3 = −8x + 3**:
This equation is an identity, as both sides are exactly equal. Therefore, this equation has infinitely many solutions.

3. **−3x − 8 = 3x − 8**:
Rearranging gives \(-3x - 3x = -8 + 8\), which simplifies to \(-6x = 0\). Dividing by \(-6\) gives \(x = 0\). Therefore, this equation has exactly one solution: \(x = 0\).

4. **−3x + 8 = −3x − 8**:
Subtracting \(-3x\) from both sides gives \(8 = -8\), which is a false statement. Therefore, this equation has no solution.

The equation with exactly one solution is:

**−3x − 8 = 3x − 8**.