Lesson Page

Math A

Solving Equations
page 2

 

Sometimes we get equations which have multiple terms on the same side.  Before we can solve these, we need to combine all the similar terms.

Solve for y:   7y + 5 - 3y + 1 = 2y + 2
 
First combine the similar terms on the left side.
We'll start with 7y and -3y.
(Don't forget to take the sign in front of the term.  If there isn't a sign in front of the term, it is considered +.)
7y - 3y = 4y.  So we have:

Now combine +5 and +1.  We get:

Now proceed as before.

  

 

7y + 5 - 3y + 1 = 2y + 2
 

 4y + 5 + 1 = 2y + 2

 4y + 6 = 2y + 2

4y + 6 = 2y + 2
-2y       -2y
2y + 6 =       2
     -6          -6
2y      =      -4
   
     y   =  -2

 

We also come across equations with parentheses.  The first step here is to multiply and get rid of the parentheses. 

Solve for n:   3(n - 1.8) = 2n + 1
First multiply the parentheses
by 3.  We get:

Now proceed as normal.

  3(n - 1.8) = 2n + 1
   3n - 5.4 = 2n + 1

   3n - 5.4 = 2n + 1
  -2n         -2n
   n - 5.4   =       1
     + 5.4        + 5.4
      n       =    6.4

 

 

Our last type of equation contains fractions.  These will be much easier to do if your scientific calculator has a fraction key.  Look for a button which says

This key will allow you to enter a fraction without changing it to a decimal.  Here's how you would enter into the scientific calculator.

3

4

The calculator will display     

 

Now you can solve equations like the following:

Solve for p:
First subtract the fraction from both sides.  Use the calculator to do the arithmetic.
2 - 1 3
  
Now divide both sides by 2.  Again, let the calculator do the arithmetic.   
1

+

 2
3 2

=

 

 


   Murray