how can I know when to add, subtract, multiply or divide an equation?

Answer 1

Rule 1: First perform any calculations inside parentheses.

Rule 2: Next perform all multiplications and divisions, working from left to right.

Rule 3: Lastly, perform all additions and subtractions, working from left to right

Answer 2

Adding and subtracting are simple. You can move any term from one side of the equals sign to the other if you change its sign. This is called transposition.

For example 2x-3 = 7
2x = 7+3=10,or another example:
2x+ 5 -a = x +2a
2x - x = 2a+a-5
x = 3a-5

If you have 3x + 5 = 11
3x = 11-5 =6
Now you must divide both sides by three to get x by itself:
3x/3 = 6/3
x=2

x/6 -5 = 6
x/6 =6+5 = 11
Now you must multiply both sides by 6 to get x by itself:
6x/6 = 6*11
x = 66

That's all there is to it.

Answer 3

Consider the equation:
4(x + 3) - 25 - x = 4x - 15
First expand the brackets:
4x + 12 - 25 - x = 4x - 15
Combine any x terms on the same side of the equal sign:
3x + 12 - 25 = 4x - 15
Combine any numerical terms on the same side of the equal sign:
3x - 13 = 4x - 15
Now you have just one x term and one numerical term on each side.
Aim to collect x terms on the left, and numerical terms on the right.
Subtract 4x from each side leaving just numbers on the right:
- x - 13 = -15
Add 13 to each side leaving just x terms on the left:
-x = -2
Multiply by -1 to get x on its own:
x = 2.

You have to look at each equation individually, and decide what is the most suitable sequence of operations. No set of rules can always give you the steps in the right sequence for every situation.