The Math Forum

Ask Dr. Math - Questions and Answers from our Archives
Associated Topics || Dr. Math Home || Search Dr. Math

Solving Simple One-Variable Equations

Date: 02/14/98 at 18:10:56
From: krissie
Subject: Algebra solving equations

    n+39 = 12
  w+(-8) = -21
      24 = m-8.6
      18 = 7-p
    -5/9 = w-(3/4)
     -6n = 16
    3/4w = -48
    - 13 = n/-4
    9-4w = -11
 p/-6 +7 = -14    

I need help on how to work these problems out and get the answer. 
Can you help me?

Date: 02/19/98 at 13:20:57
From: Doctor Loni
Subject: Re: Algebra solving equations

Solving equations can be tough when you are first getting started, but 
don't despair, you'll get there!  Let's see if I can help you along.

In these equations, the letter (like n or w or p or x or y, etc.) 
really stands for a number that will make the number sentence true. 
The goal is to find out what that number is.

For instance, if you had an equation that said

       x + 2 = 5

what it is really asking is "what number when I add 2 to it will give 
me 5?"  You could probably do that one in your head, because you know 
that 3 + 2 = 5, therefore x = 3.

You can't always do it in your head, however, so there are techniques 
you can use to find out what number the letter represents.  Some 
things to remember:

1. The equals sign means just that - whatever is to the left of the 
   equals sign has the same value as whatever is on the right side of 
   the equation.

2. You can do whatever you want to an equation - add to it, subtract 
   from it, multiply it by something, divide it by something, as long 
   as you do the same thing to both sides! That way it stays equal.  
   For instance if:

         3 + 2 = 5

   I can add 2 to both sides of the equation and it will still be true:

     3 + 2 + 2 = 5 + 2       
             7 = 7

3. You want to get the variable (the letter) on one side of the 
   equation all by itself, because then you will know what it is equal 
   to. So, for instance in the first problem, you will end up with 
   n = something and that will be your answer.

Okay, with that as a little background, let's try a few.

     n + 39 = 12

We want to get n by itself on one side of the equals sign. Right now 
it has a 39 added to it. So to get n by itself we can subtract 39 
(from both sides of the equation remember!) and get:

     n + 39 - 39 = 12 - 39

If we do the math 39 - 39 = 0 and 12 - 39 = -27 so we get:

      n + 0 = -27 or      
          n = -27

If you are having trouble adding and subtracting integers, remember 

If you are adding two positives, add the numbers and the sign of the 
answer will be positive.

If you are adding two negatives, add the two numbers and the sign of 
the answer will be negative.

If you are adding a positive and a negative, subtract the littler 
number from the bigger number and the sign will be whatever the sign 
is on the bigger number.

   i.e. 12 - 39  subtract 12 from 39, (39-12)  = 27 and take the sign 
   of the larger number --the larger number is 39 and it is negative 
   so the answer is -27.

Let's try another one:

     w + (-8) = -21

We want the w by itself on one side of the equation. Right now it has 
a -8 added to it. If we add 8 to both sides:

     w + (-8) + 8 = -21 + 8

the -8 + 8 = zero , -21 +8 = -13 and we get

     w + 0 = -13 or
         w = -13

Let's try one with some multiplication:

       -6n = 16

We still want to get n by itself on one side of the equals sign, but 
in this case it is multiplied by a -6, so it is really saying we have 
-6 n's. We only want one n not -6 of them, so what can we do that will 
get us just one n? If we divide both sides by -6:

    -6n/-6 = 16/-6

     -6/-6 = 1 so we will have just one n which is what we want:

        1n = 16/-6

With just 1n we normally leave off the 1 because it is understood when 
n is by itself there is only one

     n = 16/-6  or 
     n = -16/6    
(with a negative fraction, the minus sign is usually put in the 

If your teacher requires the answer in lowest terms, you will need to 
reduce that fraction.

Let's do one more:

     -13 = n/-4

Once again, we want to get n by itself on one side of the equation (it 
doesn't matter which side as long as it is by itself). In this case n 
is divided by a -4.  Again, we want just one n. So if we multiply both 
sides of the equation by -4

 -4(-13) = (-4)n/-4
   -4/-4 = 1 and 
 -4(-13) = 52 so
      52 = 1n or
      52 = n

I hope this helps a little. Let me know if you have any more questions 
or are having any trouble, adding, subtracting, multiplying and 
dividing integers.

-Doctor Loni,  The Math Forum   
Associated Topics:
Middle School Algebra

Search the Dr. Math Library:

Find items containing (put spaces between keywords):
Click only once for faster results:

[ Choose "whole words" when searching for a word like age.]

all keywords, in any order at least one, that exact phrase
parts of words whole words

Submit your own question to Dr. Math

[Privacy Policy] [Terms of Use]

Math Forum Home || Math Library || Quick Reference || Math Forum Search

Ask Dr. MathTM
© 1994- The Math Forum at NCTM. All rights reserved.