combining like terms

The main concept to drive home here is the order of operations, or what most people might recall as the accronym: PEMDAS... Which stands for
**P**arenteses, **E**xponents,** M**ultiplication,
**Di**vision, **A**ddition, **S**ubtraction. PEMDAS pretty much tells us the order of priority in which we do the operations as they are listed above. We do anything inside a parenteses first, then we take care of exponents, then we do multiplication/division depending on which one is the leftmost operation. Some people would argue that multiplication always takes a higher priority, but that is what we have parenteses for. Then last we have addition/subtraction.

We start working on this expression very much like the way we read: from left to right and look for what is going to come up first according to our accronym...

So here we go.

In 7(2x - 4) -(10 - 3x) We see a 2x - 4 in the parenteses we can't combine those since they do not have like terms... same follows for the 10 - 3x in the other parenteses so we move... So what is next. Multiplication. Lets take care of that then.

the 7 is being multiplied by (2x - 4), so we have to distribute. This yields:
14x - 28

we also have -(10 - 3x) that - sign is really a -1 remember this as it will save you from droping a negative sign in the future. In reality the expression we really started with can be seen like this to avoid dropping minus signs 7(2x - 4) + -1(10 - 3x). Anyways we get -10 + 3x when we distribute the negative 1.

This gives us 14x - 28 - 10 + 3x, at which point we add the 14x and the 3x together to get 17x, and the -28 and the -10 to get -38 because they are like terms.

One more time with out the descriptions:

7(2x - 4) - (10 - 3x)

14x -28 + 3x - 10

17x - 38