Question

Which equations have no solution? (choose 2)
Responses
A -20 = -4x – 6x-20 = -4 x – 6 x
B 4m – 4 = 4m4 m – 4 = 4 m
C 6x + 1 = -6(1 – x)

6 x + 1 = -6(1 – x )
D 6 = 1 – 2n + 56 = 1 – 2 n + 5
E -(7 – 4x) = 9

Answer 1

To determine which of the given equations have no solutions, we can simplify each equation and analyze them.

A. **-20 = -4x - 6x**
- Combine like terms: -20 = -10x
- Dividing both sides by -10 gives: x = 2
- This equation has a solution: x = 2.

B. **4m - 4 = 4m**
- Subtract 4m from both sides: -4 = 0
- This is a contradiction, meaning the equation has no solution.

C. **6x + 1 = -6(1 - x)**
- Distributing on the right: 6x + 1 = -6 + 6x
- Simplifying gives: 6x + 1 = 6x - 6
- Subtracting 6x from both sides: 1 = -6
- This is a contradiction, meaning the equation has no solution.

D. **6 = 1 - 2n + 5**
- Combine like terms: 6 = 6 - 2n
- Subtracting 6 from both sides: 0 = -2n
- Dividing both sides by -2 gives: n = 0
- This equation has a solution: n = 0.

E. **-(7 - 4x) = 9**
- Distributing the negative: -7 + 4x = 9
- Adding 7 to both sides: 4x = 16
- Dividing by 4 gives: x = 4
- This equation has a solution: x = 4.

Based on this analysis, the equations with no solution are:

**B** and **C**.