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.