How to Solve Linear Equations

Linear equations are the most basic algebraic equations that you will see in Algebra I.  These types of equations are number sentences that contain variables and the point of the equation is to find the value for the variable.  For example, in the equation x + 3 = 8, you need to find the value of “x” because “x” is the variable.  All linear equations will have numbers and variables.  For the purpose of this lesson, we will learn how to solve linear equations with only one variable.

In order to find the value of the variable, you need to perform operations (math steps) that will lead you to having the variable all by itself on one side.  How do you do that?  Follow these easy steps and you will know exactly how to solve for the value of a variable in any one-variable linear equation problem!

Step #1:  Get the variable by itself by either adding, subtracting, or dividing the number that is on the same side as the variable. 

Whatever you do to one side (add, subtract, or divided), you need to do to the other side!!!  You have to fair to each side! J

Ex)  x + 3 = 5    How do you get “x” by itself?  In this problem you need to subtract “3” from each side.

      x + 3 =  5

          - 3 =  5 - 3

    __________

Step  #2: Perform the appropriate operation.  Add, subtract, or divide.

Ex)  x + 3 = 5

            - 3 = 5 - 3

       ________

        x = 5 – 3

Step #3:  Solve!

Ex)  x = 5 – 3

        x = 2

Step #4:  Plug in the value of the variable to determine if the equation makes sense and is a correct answer.

Ex)  If “x” equals 2, then plug in “2” for “x” in the linear equation x + 3 = 5

      x + 3 = 5

      2  + 3 = 5    Does this make sense?  Does 2 + 3 = 5?  Yes!  You solved for “x” correctly!

Let’s try another example!

Ex)  5x – 5 = 25     How will I get “x” by itself in this problem? 

Step #1:  Get all the numbers to one side, remember?

5x – 5 = 25

5x + 5 = 25 + 5

Step #2:  Perform the operation!

5x – 5 = 25

5x + 5 = 25 + 5

____________

5x = 30    OK, but you still have a number with the variable “x”  Repeat Steps #1 and #2 to get “x” by itself.

5x = 30 (how will you get “x” by itself?  You need to divide by 5 on both sides!)

5x = 30

5        5

Step #3: Solve for “x”

x = 6

Step #4:  Plug in the value of “x” to the original equation.

Ex) 5x – 5 = 25

      5(6) – 5 = 25

      30 – 5 = 25    Is this correct?  Does it make sense?  YES!!! J 

Congratulations!  Now you know how to solve basic linear equations!