To isolate a variable x, we have to get the x by itself on one side of the equation, and everything else on the other side of the equation. We do this by using a number of steps to "neutralize" the numbers attached to x.

When you are dealing with equations, you have to imagine that you have an old fashioned weigh scale, with say, 6 apples in each pan. If you divide the number of apples in the left pan by 2, you will have 3 apples in the left pan and still 6 in the right pan. The left pan will shoot up into the air, and the right pan will hit the table. To balance it again, you have to do exactly the same to the right pan as you did to the left, ie. you must also divide the number of apples there by 2.

6 apples = 6 apples

6 apples ÷ 2 ≠ 6 apples

6 apples ÷ 2 = 6 apples ÷ 2

(Please note, I am a mathematician, not an artist!)
This holds true for all operations. If you add 2 apples to the left pan, you must also add 2 to the right, if you subtract 2 or multiply by 3 on the left hand side, you must do EXACTLY the same to the other side, or the scale won't balance.

THIS IS YOUR PRIME DIRECTIVE.
WHATEVER YOU DO TO ONE SIDE OF AN EQUATION IN MATH, YOU MUST DO EXACTLY THE SAME TO THE OTHER SIDE,OR IT WON'T BALANCE.

Lets look at the examples

ADDITION
x + 2 = 6
x has 2 added to it, so we need to remove the number 2 by "neutralizing" it.
If we subtract 2 from both sides, look what happens:
x + 2 - 2 = 6 - 2
x = 4
Notice that we have done the opposite operation. When x has a 2 added to it, we subtract 2 to "neutralize" it.

SUBTRACTION
x - 2 = 6
x has 2 subtracted from it, so we need to remove the number 2 by "neutralizing" it.
If we add 2 to both sides, look what happens:
x - 2 + 2 = 6 + 2
x = 8
Notice that we have done the opposite operation. When the x has a 2 subtracted from it, we add 2 to "neutralize" it.

MULTIPLICATION
10x = 20
x is multiplied by 10.
If we divide both sides by 10, the 10 cancels out, because 10 divided by 10 is 1.

Cancelling the 10's

Answer:
 x = 2
Again we have done the opposite operation. When the x is multiplied by 10, we divide by 10 to "neutralize" it.

DIVISION

x is divided by 6
If we multiply (the dot means multiply) both sides by 6, the 6's cancel because 6 divided by 6 is 1.

Cancelling the 6's

Answer:
  x = 24
Again we have done the opposite operation. When the x is divided by 6, we multiply by 6 to "neutralize" it.

If you have both multiplication/division and addition/subtraction in the same question, you do the addition/subtraction first, and then the division/multiplication. If there are brackets as well, you do those last.

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