The Math Forum

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

One Variable Equations with Decimals

Date: 02/11/97 at 00:41:57
From: Charnesha 
Subject: Algebra 1

I know how to solve equations, but I came across two in my math book 
that I have no clue about how to solve.  I have tried doing it the way 
my teacher showed me, but this type of equation is different from any 
I have ever solved. I don't know where to begin.  Please help.  
a)  8.25x + 3 = 17.5 + x

b)  x + 17.5 = 8.25x + 3

Date: 02/11/97 at 02:00:54
From: Doctor Mike
Subject: Re: Algebra 1

Hello Charnesha,
One thing you probably noticed is that these 2 equations are
essentially the same. To make one look more like the other, just 
switch left and right sides and reverse the addition order. 
So, lets just look at the first one.  An equation involving x is just 
a clue about a mystery number known only as x.  If you make the most 
of that clue, you can find out what x must be. 
An equation "left_side = right_side" just says that it is true that 
the expressions on the 2 sides of the equal sign are the same. One of 
the most important principles of high school algebra is that if you 
have a true equation, and you do EXACTLY the same thing to both sides, 
then what you get is also a true equation.
Let's see how this works for 8.25x + 3 = 17.5 + x.  I still do not 
know what x is, but I do know it is supposed to be some number. I want 
to (you will soon find out why) subtract that unknown mystery number 
from both sides of the equation.  On the left I have 8.25 times x, and 
3, added together.  If I subtract x from that I'll only have 7.25 
times x, and I'll still have the 3, so the left side will be 
7.25x + 3.  On the right I have 17.5 and x added together.  If I 
subtract x from that I'll only have the 17.5 remaining, because adding 
the x and immediately subtracting it off again doesn't really change 
anything.  It's like adding zero.  So, the new true equation looks 
       7.25x + 3 = 17.5   
The next step is just like the first, only different!  What I mean is 
that again I will be doing EXACTLY the same thing to both sides of the 
equation, to get another new true equation. What's different is the 
thing I do.  This time I don't subtract x from both sides, I subtract 
3.  I think you can see I'll get: 
       7.25x = 14.5 
I'm still not there yet, but I'm close.  The left side is 7.25 times 
x, and if I divide the left side by 7.25 I'll get just x. So, the 
final step is to divide both sides by 7.25.  Remember the basic 
       x = 14.5/7.25
You can either divide 14.5 by 7.25 by long division, or do it on a 
calculator.  Or maybe you observed that 7.25 is precisely half of 
14.5.  However you do it you find out the right side is 2.  So, x = 2 
is a true equation that gives you the value of the mystery number x.  
I hope this helps.  Have fun in Algebra 1!  

-Doctor Mike,  The Math Forum
 Check out our web site!   
Associated Topics:
High School Basic 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.