Solving Equations with Variables on Both Sides

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

Subtraction in Equations

Preview

Subtracting equations is just another way to say subtracting equations with variables in them.
Like for example if we have the equation "y-4=15" with the variable y which is a lower-case letter.
To solve this we have to add since it is the opposite of subtraction and we have to add the +4 like this:

 y-4=15

  +4   +4

Now we are left with 15+4 since the 4's since -4+4 cut each other out like this:

 y-4=15  =   15

  +4   +4     + 4

                  -----

 y      =        19

So now we have a statement that says 15+4=19 and that y=19 and to find out if this is true we have to put our answer into the previous equation like this:

19-4=15

y=19

So this statement is true.
Now try some of these and make sure to watch the video on YouTube.

Sheet 1 Subtracting Equations