Associated Topics || Dr. Math Home || Search Dr. Math

### 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

-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/
```
Associated Topics:
Middle School Algebra
Middle School Equations

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