Variables on Both Sides
Below is a great video found by a group that presented on multi-step equations.
Combining Like Terms
Solve equations with more than one like term the same way that you simplified expressions with more than one like term.
x + 3 + 4 + 5x - 6 + (-8x) = 1 + -9 Look for all the terms that are the same and pay
attention to the sign in front of each one.
x + 5x + -8x can go together to make -2x
3 + 4 - 6 can go together to make 1
1 + -9 can go together to make -8.
Notice that you can't combine terms that are on opposite sides of the equation because the equal sign is separating those terms. You can only combine those terms by using the inverse operation.
We simplified the equation to look like -2x + 1 = -8
Following the order of operations, we would multiply 2 and x together first, then subtract 1, so to solve the equation we work backwards using the inverse operation for each step. This means we will add 1 first, then divide x by 2.
-2x + 1 = -8
-2x = -9
x = 4.5 or 4 1/2
A video from a student explains this concept perfectly.
This type of equation can be confusing if you don't understand that we are working with the order of operations (PEMDAS) in reverse. This means that whatever you would do first when you simplify the expression would now come last as its inverse. Below are a couple examples and a very helpful video.