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

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

6x+3=−6x+3

Answer 1

To determine which equation has no solutions, we can analyze each option:

1. **−6x + 4 = −6x + 3**
- If we try to isolate the variable, we can add 6x to both sides:
- 4 = 3 (This is not true.)
- **Conclusion:** This equation has no solutions.

2. **−6x + 4 = 6x + 3**
- Rearranging gives:
- −6x - 6x = 3 - 4
- -12x = -1
- x = 1/12
- **Conclusion:** This equation has a solution (x = 1/12).

3. **6x + 4 = 6x + 4**
- Subtracting 6x from both sides gives:
- 4 = 4 (This is always true.)
- **Conclusion:** This equation has infinitely many solutions.

4. **6x + 3 = −6x + 3**
- Rearranging gives:
- 6x + 6x = 3 - 3
- 12x = 0
- x = 0
- **Conclusion:** This equation has a solution (x = 0).

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

**−6x + 4 = −6x + 3**.