How do you solve an equation for a given variable? For example, how would you do: 5(2m+3) -(1-2m) = 2[3(3+2m) - (3-m)]

We'll start by removing the brackets both
sides:

5(2m+3) -(1-2m) = 2[3(3+2m) -
(3-m)]

10m + 15 - 1 + 2m = 6(3+2m) -
2(3-m)

Now, we'll remove the brackets form the right
side:

10m + 15 - 1 + 2m = 18 + 12m - 6 +
2m

We'll subtract 18 both
side:

10m + 15 - 1 + 2m - 18 = 18 - 18 + 12m - 6 +
2m

10m + 15 - 1 + 2m - 18 = 12m - 6 +
2m

We'll add 6 both sides:

10m
+ 15 - 1 + 2m - 18 + 6 = 12m - 6 + 6 + 2m

10m + 15 - 1 + 2m
- 18 + 6 = 12m + 2m

We'll combine like terms from the right
side:

10m + 15 - 1 + 2m - 18 + 6 = 14
m

We'll subtract 14m both
sides:

10m + 15 - 1 + 2m - 18 + 6 - 14m =
0

We'll combine like terms
again:

-2m + 2 = 0

WE'll
subtract 2 both sides:

-2m =
-2

We'll divide by
-2:

m =
1