Simplifying Expressions

Date: 11/24/97 at 02:23:53
From: Jacques Thurman
Subject: Regarding Simplifying Expressions

Hello Dr. Math,
My name is Lisa Pagan and I am in 9th Grade. I am stuck on lots of 
problems but I really need your help on this one particular problem:

   2x - ( 3 - x ) =  x - 7

Date: 11/24/97 at 16:07:31
From: Doctor Bruce
Subject: Re: Regarding Simplifying Expressions

Hello Lisa,

I would guess that you want to "solve" this equation for x. That means
you would like to find a number to substitute for x which will make 
the equation true.

It helps to understand that all the fancy symbols we use in algebra 
are just different names for numbers. We can add and subtract with  
"x" because we can add and subtract with numbers, and "x" is going to 
turn out to be some number.

Here's what we do. First, we apply the Distributive Law to the 
parentheses. The negative sign has to be distributed over both the  
3 and the -x which are inside the parentheses. After we do that, the 
equation looks like

     2x - 3 + x = x - 7

We see that there is an x term on both sides of the equation, so we 
can subtract x from both sides (remember, x is just a number!) to get

         2x - 3 = - 7

The strategy, you see, is to isolate the x term by itself on the left 
side of the equation. Let's add 3 to both sides now - this will get 
rid of the -3 on the left side. Now we have

             2x = -4.

We're pretty close now. We know that twice the number x equals  -4, so 
let's divide both sides of the equation by 2. Then we have

              x = -2.

It looks like the answer we wanted is x = -2. What you should do now 
is go back to the original equation and substitute the value -2 for x  
to see that you get a true statement. You should get the value -9 for 
both sides of the equation. Since -9 = -9 is a true statement, you 
have checked that your answer x = -2  is correct.

Good luck with your future equations,

-Doctor Bruce,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/