s

[magikarp]

I'll explain in general, and if you want an explanation on a particular questions you can just ask. (But feel free to ignore the explanation if you're not interested.)

Say you have some equation, like x - 5 = 11. You want to know what x is. This one is easy enough to do mentally--if 5 less than x is 11, x must be 16. But for more complicated equations it's difficult to do that. Instead, you can change the equation so that you have x = [some expression], but you have to make sure that both sides of the equation remain equal. You can, for example add something to or subtract something from both sides of an equation, and they will still be equal. If you add 5 to each side of x - 5 = 11, you get x + 0 = 16. This is the same as x = 16, and that's what we're looking for.

Multiplying and dividing work in the same way. Take 5x = 20. It's pretty obvious this is 4, but just pretend it's not obvious. If we divide each side by 5, the equation remains true, and we get x = 4. Or x/3 = 2. Multiply each side by 3 to get x = 6.

The only sort of tricky thing is that if I do something to each side of the equation, I have to do it to the whole expression. If I have x/3 + 3 = 6, it would be untrue to say x + 3 = 18. If I wanted, I could do something like this:

3(x/3 + 3) = 6*3
x + 9 = 18
x = 18-9
x = 9

It's more common, though, to just take care of the addition and subtraction first:

x/3 = 6 - 3
x/3 = 3
x = 3*3
x = 9

(I feel like I should say that you can add or subtract whatever number you want, or multiply and divide by any number but zero, even if it doesn't help you get x alone, and the equation will still be true. It just might not help you solve the equation, and your teachers will likely think you're silly.)

Hidden stuff:

I'm guessing at some of the questions here, because how you wrote it confused me. It should be fine if you check them first.

12 = (a/ 36) + 17
12 - 17 = a/36
-5 = a/36
36(-5) = a
-180 = a

18 - r = 42
-r = 42 - 18
-r = 24
r = -24

80 = 23 - 3v
80 - 23 = -3v
57 = -3v
57/-3 = v
-19 = v

-2q - 63 = 47
-2q = 47 + 63
-2q = 110
q = 110/-2
q = -55

(-x /2) + 4 = 12
-x/2 = 12 - 4
-x/2 = 8
-x = 8 * 2
-x = 16
x = -16

-5 = -19 - (x/7)
-5 + 19 = -x/7
14 = -x/7
7*14 = -x
98 = -x
-98 = x