The Math Forum

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

Solving x-(-16) = 0

Date: 02/17/98 at 23:11:30
From: Ashley
Subject: Algebra (addition, and subtraction)

My question will probably be considered quite simple but all I need is 
the answer and I can figure it out. Here goes:

   x- -16 = -16

I'm totally clueless and it's just my luck that my math page got 
ripped out of my text so I have no instructions. Thanks!
Confused Girl,

Date: 04/16/98 at 12:53:12
From: Doctor Morrell
Subject: Re: Algebra (addition, and subtraction)


Hi, my name is Matt, I'm a senior in high school, and I'm going to try 
to help you better understand these types of problems. What you're 
asking can be confusing at first, but with practice these problems 
become second nature. 

First let's change the problem. Instead of x- -16 = -16, we'll use:

   x- -12 = -12

The first thing that we need to discuss is sign changes.  You have 
probably already been taught these, but I just want to refresh your 

If you have two negative signs right beside each other, they 
become positive:

   4- -5 = 4 + 5 

If you have a positive and a negative right beside each other, they 
become negative:

   4+ -5 = 4 - 5    

If you have two positive signs right beside each other, they
become positive:

   4+ +5 = 4 + 5    
If you have a negative and a positive right beside each other, they 
become negative:
   4- +5 = 4 - 5   

If you look at your problem, that is all you are doing. You're 
simplifying the signs by the rules above. 

So take:

   x- -12 = 0

As you can see, there are two negatives (-) right beside each other so
the two negatives become a positive, and:

   x- -12 = 0    becomes   x + 12 = 0

The last thing that you have to do is solve for zero. It may sound 
complicated, but trust me, all you do is change the sign and move it 
across the equal sign.

What you do for solving zero is move your 12 to the other side.  
Because 12 is positive you must subtract it FROM BOTH SIDES. Make sure 
that you subtract from BOTH sides or your answer will come out wrong:

    x + 12  =   0   
       -12    -12
    x +  0  = -12

The answer can be rewritten as:  x = -12.

The exact same process is used in your problem. I'll give you some 
practice problems that you can try.  

   questions:                   answers:

   x- -7 = 0                      x = -7     
   x- -1 = 0                      x = -1   
   y- -9 = 0                      y = -9

These types of problems become VERY important in later math classes.  
Good luck to you in the future.  

-Doctor Morrell,  The Math Forum
Check out our web site!   
Associated Topics:
Middle School Algebra
Middle School Negative Numbers

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.