Solving Equations with Variables on both Sides: Example
Let’s say that we have the following equation:
4x – 5 + 3 = 2x + 1
First we have to combine like terms. So, we will combine
constants with constants and variables with variables.
Step 1:
4x – 5 + 3 = 2x + 1
4x – 2x = - 5 + 3 – 1
The reason I changed
the signs when moving the variables and constants is because if I bring a
positive to the other side it becomes negative and if I bring a negative to the
other side it becomes a positive.
Next we have to simplify.
Step 2:
4x – 5 + 3 = 2x + 1
4x – 2x = - 5 + 3 - 1
2x = + 3 – 6
2x = - 3
Note: In order to
simplify all I did was subtract the variables to get 2x and add
-5 + 3 -1 to get -3
Step 3:
4x – 5 + 3 = 2x + 1
4x – 2x = - 5 + 3 - 1
2x = + 3 – 6
2x = - 3
Now we have a one-step equation. So, we’ll have to divide 2x by 2 and -3 by 2.
4x – 5 + 3
= 2x + 1
4x – 2x = -
5 + 3 - 1
2x = + 3 –
6
2x/2 = - 3/2
x = - 3/2 or –1 1/2
