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
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