My Math Forum  

Go Back   My Math Forum > High School Math Forum > Algebra

Algebra Pre-Algebra and Basic Algebra Math Forum


Reply
 
LinkBack Thread Tools Display Modes
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
xx3004 is offline  
 
December 22nd, 2010, 05:38 PM   #2
Global Moderator
 
Joined: Dec 2006

Posts: 20,469
Thanks: 2038

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.
skipjack is offline  
December 22nd, 2010, 05:56 PM   #3
Member
 
Joined: Dec 2010
From: Viet Nam and US

Posts: 36
Thanks: 0

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
xx3004 is offline  
December 22nd, 2010, 06:10 PM   #4
Global Moderator
 
Joined: Dec 2006

Posts: 20,469
Thanks: 2038

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.
skipjack is offline  
December 22nd, 2010, 07:33 PM   #5
Member
 
Joined: Dec 2010
From: Viet Nam and US

Posts: 36
Thanks: 0

Re:

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!
xx3004 is offline  
December 22nd, 2010, 07:48 PM   #6
Global Moderator
 
Joined: Dec 2006

Posts: 20,469
Thanks: 2038

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.
skipjack is offline  
December 22nd, 2010, 08:09 PM   #7
Member
 
Joined: Dec 2010
From: Viet Nam and US

Posts: 36
Thanks: 0

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).
xx3004 is offline  
December 22nd, 2010, 08:52 PM   #8
Global Moderator
 
Joined: Dec 2006

Posts: 20,469
Thanks: 2038

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.
skipjack is offline  
December 22nd, 2010, 09:00 PM   #9
Member
 
Joined: Dec 2010
From: Viet Nam and US

Posts: 36
Thanks: 0

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!
xx3004 is offline  
Reply

  My Math Forum > High School Math Forum > Algebra

Tags
inequality, solve



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
solve the inequality: x-2|x|>2 mattematicarka Algebra 2 February 6th, 2013 11:22 AM
Solve an inequality hence solve another inequality Punch Algebra 3 July 2nd, 2012 12:43 PM
Solve the Inequality. jatt-rockz Algebra 5 November 10th, 2011 05:07 AM
How to solve this inequality ? silvercats Linear Algebra 13 June 6th, 2011 07:48 AM
how to solve this inequality sikwn32 Algebra 5 August 30th, 2009 02:12 PM





Copyright © 2019 My Math Forum. All rights reserved.