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Solving Equations with Variables on both sides

 

     When you solve an equation, you are solving to find the number that is missing.  This missing number is usually shown as a letter (variable).  You have to find the value of the letter (variable) that is missing to solve the equation.

___________________________________________

 

Rules for Solving Equations with variables on both sides of the equal sign:

 

Step 1:  Identify the variables.

 

          Variable-  the letter in the problem, its what you are solving for

     it can be any letter, NOT JUST X OR Y

 

       For example: 

 

                   1.  2x  +  20  =  100 + 4x                 X  IS THE VARIABLE

 

                   2.  3m +  7  =  13 - 3x                     M  IS THE VARIABLE

 

 

 

          You try:  Identify the variable

 

                   1.  2x  +  18  =  36 - 4x                    ___________________

 

                   2.  20  -  9n  =  27 + 2n                   ___________________

 

                   3.  15t  +  5  =  100 - 10t                 ___________________

  Hint:  Remember that you have to get the variable by itself to find the answer!!  *

 

Step 2:  Add/Subtract whole numbers so theyre all on one side.

          (What you do to one side you MUST do on the other side.)

 

        For example:

Text Box: Hint: 
Do the opposite operation that is in the equation.  
Here you would add + 5 to both sides of the = sign.

 

 

 


 

         

 

 

5x

-  5

=

     x

     +         15

 

+ 5

 

 

          +5

5x

 

=

     x

             20

 

 

 

Step 3:  Add/Subtract Variables so theyre all on one side.

 

 

5x

 

=

    x

   +    20

  -  x

 

 

 -  x

 

4x

 

 =

 

20

 

 

Step 4:  Multiply /Divide to get the variable by itself.

 

Text Box: Hint:  
Do the opposite operation that is in the equation.  
 
Here you would DIVIDE   4 to both sides of the = sign.
 

 

        For example:

 

    4x

=

     20

  4

=

  4

X

=

    5

 

 

 

 

 

 

          ANSWER SHOULD BE WRITTEN:  X = 5

 

Step 5:  Check your work.

       (Do this by plugging the value of your variable back into the equation.)

 

                5x  -  5  =  x  +  20              (5  5) 5  =  x  +  15

                                                       25 5      =  5  +  15

                                                                    20        =       20

                                                   The answer is correct!  J


 

Examples of How to Solve Equations with Variables on both sides

 

1.   3y +  9  = 9x  -  18

 

 

 

 

 

2.  2m +  11   =  4m  +  1

 

 

 

 

 

3.  5f   +   5   =  f   +   20

 

 

 

 

 

4.  9d  -  5    =  4d  +  35

 

 

 

 

 

5.  10x    2  =  3x  +23

 

 

 

 

 

6.  11c  -  12   =  7c  +   24