Preparing for an Algebra Test

Date: 11/1/95 at 9:29:18
From: Anonymous

Subject: simplify (1-1/2)(1-1/3)(1-1/4)...(1-1/n)

Dear math doctors,

I am in the ninth grade at the moment and I am schooling in Durban 
Girls College, South Africa.  My final exams are starting in less 
than 2 weeks and so I'm preparing very hard for them.  I have to 
do extremely well in my mathematics paper as it is my favorite, 
and I believe that Math is a subject that one can get full marks 
in.  I am very certain that with your help I will do well in my 
examination.

I have with me a copy of the last years final exam, and there are
certain questions that I don't know how to do, or some terms that 
I need explaining on.

The instructions read:

Solve for x:

a) 2 1/2x = 95

b) 7/x - 3 = 5/x + 2

What is the difference between the terms: solve and simplify?  If 
I know that, perhaps I could do the sum.

How do you find the gradient in a graph?  I know that an equation 
for a straight line graph is y = mx + c, but how do you find the 
gradient and where the graph cuts the axes?

How do you find the line parallel to this one: x - 2y = 3 which
passes through (0;-1).

Another section that I do not understand is the real number system 
of set builder notation.  Perhaps you could send me hints on that 
as well.

Well, this is very urgent and if you will help me (which I'm sure 
you will) I shall be most grateful.  I am really glad that I can 
write to Dr. Math to clarify my problems.  The only problem I find 
is transferring the questions to you.  But as I use this network I 
will find out.

Please send me replies as soon as possible.

Yours
Ruta Nerlekar
e-mail address:
nerlekar @ iafrica.com
DR M G NERLEKAR
DURBAN.
031,210858/2026892/

Date: 11/19/95 at 16:55:50
From: Doctor Ken
Subject: Re: simplify (1-1/2)(1-1/3)(1-1/4)...(1-1/n)

Hello!

>The instructions read:
>
>Solve for x:
>
>a)2 1/2x = 95
>

Is this "two and one-half x," or is this "two times one-half x," 
or is this "twenty-one over two x" (probably not).  I bet that no 
matter which one of these it looks easier to do than your next 
question, so I'll give you a hint on it:

>b) 7/x - 3 = 5/x + 2
>
Try multiplying through by x to get the equation:
7 - 3x = 5 + 2x.  Is that easier?

>What is the difference between the terms: solve and simplify? If 
>I know that perhaps I could do the sum.

Usually, solve means "find the value of x which makes this 
equation true," and simplify means "take this equation or 
expression and work on it until it looks simpler, easier to 
understand, and smaller." 
>
>How do you find the gradient in a graph?  I know that an equation 
>for a straight line graph is y = mx + c ,but how do you find the 
>gradient and where the graph cuts the axes?

I assume that when you're using the term "gradient," you're 
talking about the thing that I would call "slope."  Tell me if I'm 
wrong.  If you have an equation in the form y = mx + b, the slope 
is m, and it intersects the y axis at the point (0,b).  That's 
because the y-axis is where x is zero, so you plug in zero for x 
and you get y = m*0 + b = b.  To find out where the line hits the 
x-axis, you'd plug in zero for y and solve for x.

>How do you find the line parallel to this one: x - 2y = 3 which
>passes through (0;-1).

Think about this: parallel means "has the same slope."  So see if 
you can find the slope of this line, and then you're halfway 
there: all you need to do is find b, the y-intercept.

>Another section that I do not understand is the real number
>system of set builder notation. Perhaps you could send me hints 
on
>that as well.

I actually am not sure what you mean by "set builder notation."  
If you help us out and clarify, perhaps we can help you.

-Doctor Ken,  The Geometry Forum