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 December 22nd, 2010, 04:46 PM #1 Member   Joined: Dec 2010 From: Viet Nam and US Posts: 36 Thanks: 0 Inequality solve Hi guys I'm new, I need help in this topic Solve: [color=#008000] (1)[/color] I'm trying to use another variable to replace x (sorry about my English, I'm Asian, I just love math ). So I do: Let [color=#008000] (2)[/color] [color=#008000] (1)(2)[/color] And I'm stuck there  December 22nd, 2010, 05:38 PM #2 Global Moderator   Joined: Dec 2006 Posts: 20,931 Thanks: 2207 Where did "-10t" spring from? You have 3x = t� - 2, so multiply the original equation by 3 and then substitute for 3x throughout and find the non-negative values of t that satisfy the inequality, etc. December 22nd, 2010, 05:56 PM   #3
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Quote:
 Originally Posted by skipjack Where did "-10t" spring from? You have 3x = t� - 2, so multiply the original equation by 3 and then substitute for 3x throughout and find the non-negative values of t that satisfy the inequality, etc.
I'm not sure what are you trying to help me out, could you do it for me?

About where "-10t" comes from, I mistyped, it must be "-10xt" let me explain:
We have and
The original inequality can be rewritten:
or
And that's how I came up, I need another better solution I guess  December 22nd, 2010, 06:10 PM #4 Global Moderator   Joined: Dec 2006 Posts: 20,931 Thanks: 2207 That's precisely what I gave you - multiply the original equation by 3, etc. You'll find it easy if you try it. Alternatively, plot the graph of the left-hand side of the original equation. December 22nd, 2010, 07:33 PM   #5
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Quote:
 Originally Posted by skipjack That's precisely what I gave you - multiply the original equation by 3, etc. You'll find it easy if you try it. Alternatively, plot the graph of the left-hand side of the original equation.
I've done what you told (I don't know whether I understand it correctly or not), and thanks to you, I have this:

Multiply both sides by 3, substitute and simplify:

Factor out (I don't know how to explain, just see the line below) the result, we have:

Listed the solutions orderly, we have:

So in order to make the equation satisfy, we have to pick:

But that is the way we pick t, how about x? The main reason is to solve x. I think I mislead somewhere! December 22nd, 2010, 07:48 PM   #6
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Quote:
 Originally Posted by xx3004 Multiply both sides by 3, substitute and simplify:
Your simplification was incorrect (the constant at the end should not be 10), and your factorization of the polynomial you obtained was also incorrect; the correct polynomial factorizes fairly easily. When you solve, remember that only non-negative values of t are of interest. December 22nd, 2010, 08:09 PM   #7
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Re:

Quote:
Originally Posted by skipjack
Quote:
 Originally Posted by xx3004 Multiply both sides by 3, substitute and simplify:
Your simplification was incorrect (the constant at the end should not be 10), and your factorization of the polynomial you obtained was also incorrect; the correct polynomial factorizes fairly easily. When you solve, remember that only non-negative values of t are of interest.
I see, my fault, I'm so carelessly! Now let's start over Multiply both sides by 3, substitute and simplify:

Factor out and we have:

Listed the solutions orderly, we have:

So in order to make the equation satisfy, we have to pick:

I think it's ok now, but how about x? That solution now works for t only. I'm not sure what you mean by "only non-negative values of t are of interest" (language limit I'm sorry). December 22nd, 2010, 08:52 PM #8 Global Moderator   Joined: Dec 2006 Posts: 20,931 Thanks: 2207 Your (x + 1)� should be (t + 1)�, but can be omitted (just solve 2t� + 10t + 5 ? 0). You solved incorrectly. You need t ? 0, so 0 ? t ? (-3 + ?35)/2. Hence 0 ? t� ? (22 - 3?35)/2, i.e., 0 ? 3x + 2 ? (22 - 3?35)/2, and so -2/3 ? x ? (6 - ?35)/2. December 22nd, 2010, 09:00 PM   #9
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Re:

Quote:
 Originally Posted by skipjack Your (x + 1)� should be (t + 1)�, but can be omitted. You solved incorrectly. You need t ? 0, so 0 ? t ? (-3 + ?35)/2. Hence 0 ? t� ? (22 - 3?35)/2, i.e., 0 ? 3x + 2 ? (22 - 3?35)/2, and so -2/3 ? x ? (6 - ?35)/2.
I gotcha, thank you very much Skipjack! Tags inequality, solve Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post mattematicarka Algebra 2 February 6th, 2013 11:22 AM Punch Algebra 3 July 2nd, 2012 12:43 PM jatt-rockz Algebra 5 November 10th, 2011 05:07 AM silvercats Linear Algebra 13 June 6th, 2011 07:48 AM sikwn32 Algebra 5 August 30th, 2009 02:12 PM

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