Addition and subtraction are inverse operations, as are multiplication and division.

To solve an equation means to isolate the unknown, x, on the left of the = sign.

x = The solution.

Numbers therefore must be shifted from one side of an equation to the other.  We can do that by writing them on the other side with the inverse operation.

Thus, if an equation looks like this

x + a = b,

then the solution will look like this:

x = b − a.

Since a was added on the left, we may subtract it on the right.  This is the relationship between addition and subtraction.

And similarly for each of the operations and their inverses.

Example.   Solve this equation for x:

ax − b + c − d = e

 Solution.   To isolate x, we must bring a, b, c, d to the other side.

First, bring each addition and subtraction to the right by changing each operation sign:

ax  =  e + b − c + d

This is called transposing.

Then, since a multiplies x, it will divide the other side:

See Skill in Algebra, Lesson 9.