Question

Which of the following equations has no solutions?(1 point)
Responses

−6x+4=−6x+3
negative 6 x plus 4 equals negative 6 x plus 3

6x+4=6x+4
6 x plus 4 equals 6 x plus 4

−6x+4=6x+3
negative 6 x plus 4 equals 6 x plus 3

6x+3=−6x+3

Answer 1

To determine which equation has no solutions, let's analyze each option:

1. **−6x + 4 = −6x + 3**:
If we simplify this, we can add \(6x\) to both sides:
\(4 = 3\).
This is a false statement, so this equation has no solutions.

2. **6x + 4 = 6x + 4**:
This simplifies to \(6x + 4 - 6x - 4 = 0\) or \(0 = 0\), which is a true statement for all \(x\). Therefore, this equation has infinite solutions.

3. **−6x + 4 = 6x + 3**:
If we combine like terms, we can add \(6x\) to both sides:
\(4 - 3 = 6x + 6x\) leads to \(1 = 12x\), or \(x = \frac{1}{12}\). This equation has one solution.

4. **6x + 3 = −6x + 3**:
If we add \(6x\) to both sides, we get \(6x + 6x + 3 = 3\) which simplifies to \(12x + 3 = 3\). Subtracting 3 from both sides gives us \(12x = 0\) or \(x = 0\). This equation has one solution.

Based on this analysis, the equation that has no solutions is:

**−6x + 4 = −6x + 3**.