Negative Numbers in Equations

Date: 11/20/2001 at 22:53:03
From: Stacey Merrow
Subject: Algebra

Hi! I have just recently started home schooling, and I don't know 
how to do some of the homework I am getting. Here are some examples of 
confusing equations:

  -30 = -37 + b/15
     b= ?

  -c/4 - 8 = -48
          c= ?

How do I figure out how to solve the equation?

My grandpa has helped me try to understand how to do some of them, 
but these are really confusing.

     5+r/-2 = -6
          r = 17   Is this correct?

How would I do this equation?

    -a - -3/3 = 10
            a = ?

Date: 11/21/2001 at 16:53:48
From: Doctor Sarah
Subject: Re: Algebra

Hi Stacey - thanks for writing to Dr. Math. It's always great to hear 
from a home-schooler!

Let's work through your equations. Your goal is to collect like terms 
(get the numbers together, and get the variables together) and to move 
the numbers to a different side of the equation from the variables by 
doing the same thing to both sides.

(1)                                        -30 = -37 + b/15
   add 37 to both sides of the equation:     7 = b/15
multiply both sides of the equation by 15: 105 = b

(2)                                   -c/4 - 8 = -48
    add 8 to both sides of the equation:  -c/4 = -40
              multiply both sides by 4:    -c = -160
              multiply both sides by -1:     c = 160

(3)                                   5 + r/-2 = -6
             subtract 5 from both sides:  r/-2 = -11
              multiply both sides by -2:     r = 22

    For why a negative times a negative = a positive, see the 
    Dr. Math FAQ: http://mathforum.org/dr.math/faq/faq.negxneg.html   

    For adding/subtracting positive/negative integers (you'll need
    this in problem 4), see the Dr. Math archives:

       Subtracting Numbers by Walking a Number Line
       http://mathforum.org/dr.math/problems/stephanie.09.12.01.html   

(4)                                  -a - -3/3 = 10
               simplify the fraction:  -a - -1 = 10
                                        -a + 1 = 10 
            subtract 1 from both sides:     -a = 9
             multiply both sides by -1:      a = -9

The final step when you solve any equation is to plug the number you 
get back into the equation to see if it works!  Let's try #4 to see if 
-9 is the right answer:

       -a - -3/3 = 10
     - -9 - -3/3 = 10
           9 + 1 = 10   (could you follow the shortcuts?)

Does this help?

- Doctor Sarah, The Math Forum
  http://mathforum.org/dr.math/