
After studying this lesson, you will be able to:
 Solve equations with variables on each side of the equal sign.
 Solve equations with parentheses and other grouping symbols.
Steps for Solving Equations with Variables on Each Side and with
Parentheses
1. Remove parentheses by multiplying
2. Collect like terms on each side of the equal sign
3. Get the variables together on one side of the equation and get the numbers
together on the other side of the equation.
4. Isolate the variable by "undoing" the operation (do this until the
variable is by itself)
 "undo" addition and subtraction first
 next, "undo" multiplication and division
5. Check by substituting the solution into the original equation
Example 1
2x + 4 = 6x + 8 
This equation doesn't have parentheses, but it does have
a variable each side. It doesn't have like terms to collect on either
side. 
2x + 4  2x = 6x + 8  2x 
First, we need to get the variables together. It doesn't
matter if we put them on the left side or the right side. Let's put them
together on the right side this time. To do that, we move 2x to the
other side by subtracting 2x from each side. Notice that we line up the
like terms. (2x is lined up with 6x so that it is easier to deal with.) 
4 = 4x + 8 
After collecting like terms (6x  2x) we now have an
equation where the variables are now together. Now, we work this as a
2step equation. 
4  8 = 4x + 8  8 
We need to "undo" +8, so we subtract 8 from each side.
This gives us 4 = 4x 

Now, we need to "undo" 4 times x, so we divide each side
by 4 
1 = x 
This is the solution 
Check:
substitute 1 for each x in the original equation
2 (1) + 4 = 6 (1) +8 work out each side separately
2 + 4 = 6 + 8 do the multiplying first
2 = 2
Example 2
6x  3 = 2x + 13 
This equation doesn't have parentheses, but it does have
a variable each side. It doesn't have like terms to collect on either
side. 
6x  3  2x = 2x + 13  2x 
First, we need to get the variables together. It doesn't
matter if we put them on the left side or the right side. Let's put them
together on the left side this time. To do that, we move 2x to the other
side by subtracting 2x from each side. Notice that we line up the like
terms. (2x is lined up with 6x so that it is easier to deal with.) 
4x 3 = 13 
After collecting like terms (6x  2x) we now have an
equation where the variables are now together. Now, we work this as a
2step equation. 
4x 3 + 3 = 13 + 3 
We need to "undo" 3, so we add 3 to each side. This
gives us 4x = 16


Now, we need to "undo" 4 times x, so we divide each side
by 4 
x = 4 
This is the solution 
Check:
substitute 4 for each x in the original equation
6 (4)  3 = 2 (4) + 13 work out each side separately
24  3 = 8 + 13 do the multiplying first
21 = 21
