5m-n=2m+5n ?

To solve for m and n in the equation 5m - n = 2m + 5n, we can simplify it by combining like terms:

5m - n = 2m + 5n
Subtract 2m from both sides:
3m - n = 5n
Add n to both sides:
3m = 6n
Divide by 3 on both sides:
m = 2n

Therefore, the solution to the equation is m = 2n.

5m – n = 2mn + 5n

Combine like terms on the right side of the equation:

5m – n = 2mn + 5n

5m – n – 2mn - 5n = 0

Factor the left side of the equation by grouping:

(5m – n) – (2mn + 5n) = 0

Factor out the greatest common factor from each group:

5(m – n) – n(2m + 5) = 0

Combine like terms:

5(m – n) – n(2m + 5) = 5m – 5n – 2mn – 5n

Simplify:

5(m – n) – n(2m + 5) = 5m – 2mn – 10n

Set each factor equal to zero and solve for m and n:

5(m – n) = 0

m – n = 0

m = n

n(2m + 5) = 0

2m + 5 = 0

2m = -5

m = -5/2

Therefore, the solutions to the equation 5m – n = 2mn + 5n are:

(m, n) = (n, n) or (m, n) = (-5/2, -5/2)