First, try to see what like terms are in the expression: I notice one variable, x and several constants. When we try to combine like terms, our goal is to simplify the problem so we have the above form re-written as something like ax+b. Now on to finding the coefficients a and b:
First, I would like to distribute the 7 into (2x-4):
7(2x-4) = (7*2x-7-4) = (14x-28). Now we have (14x-28)-(10-3x).
This is where the problem becomes tricky: We have to distribute the -1 implied by the expression into (10-3x). Why do this? Well consider this alone: -(10-3x). This is equal to -1*(10-3x). So distributing, we have:
-1*(10-3x)=(-1*10-(-1)*3x). Whew. Simplify the first term to get -10, and -(-1)*3x = +3x. This yields
Observe that by distributing the -1, we have converted the problem to an "addition" problem:
Now, we can omit the parentheses, as each term is added (or subtracted, same thing):
Lastly, we combine like terms and sum them, to obtain: