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 9th, 2014, 08:20 AM   #1
Newbie
 
Joined: Dec 2014
From: Clearwater

Posts: 5
Thanks: 0

Inequality problem

Here's the problem:

Solve the inequality. Express the solution set using interval notation: 3+absolute value of (1-[x/2]) is greater than or equal to 5.

Sorry, but I can't find some symbols on my keyboard. Anyway, the answers I got were x is less than or equal to -2 and x is less than or equal to 6. The correct answers are x is less than or equal to -2 and x is greater than or equal to 6. I'm not sure how they got the greater than or equal to 6 answer.

Gosh, I hope you can understand this with my lack of ability to use the correct symbols.
itiffanysphone is offline  
 
December 9th, 2014, 08:35 AM   #2
Global Moderator
 
greg1313's Avatar
 
Joined: Oct 2008
From: London, Ontario, Canada - The Forest City

Posts: 7,958
Thanks: 1146

Math Focus: Elementary mathematics and beyond
itiffanysphone, please post separate questions in their own thread. This helps to keep things organized.
greg1313 is offline  
December 9th, 2014, 09:34 AM   #3
Global Moderator
 
greg1313's Avatar
 
Joined: Oct 2008
From: London, Ontario, Canada - The Forest City

Posts: 7,958
Thanks: 1146

Math Focus: Elementary mathematics and beyond
$\displaystyle 3+\left|1-\frac{x}{2}\right|\ge5$

$\displaystyle \left|1-\frac{x}{2}\right|\ge2$

$\displaystyle \left|\frac{2-x}{2}\right|\ge2$

$\displaystyle \frac{|2-x|}{2}\ge2$

$\displaystyle |2-x|\ge4$

Case 1: 2 - x is positive, so |2 - x| = 2 - x:

$\displaystyle 2-x\ge4$

$\displaystyle -x\ge2$

$\displaystyle x\le-2$

Case 2: 2 - x is negative, so |2 - x| = x - 2:

$\displaystyle x-2\ge4$

$\displaystyle x\ge6$

So we have

$\displaystyle x\in(-\infty,-2]\cup[6,\infty)$
greg1313 is offline  
December 9th, 2014, 11:27 AM   #4
Newbie
 
Joined: Dec 2014
From: Clearwater

Posts: 5
Thanks: 0

Great! Thanks a lot! And I will post in separate threads from now on.

Also, what does that squished E symbol you used mean?
itiffanysphone is offline  
December 9th, 2014, 11:46 AM   #5
Global Moderator
 
Joined: Dec 2006

Posts: 20,927
Thanks: 2205

That symbol means "is in" (in the sense of being an element of a set). Hence n ∈ Z, where Z is the set of all integers, would mean that n is an integer.
skipjack is offline  
December 10th, 2014, 06:28 AM   #6
Newbie
 
Joined: Dec 2014
From: Clearwater

Posts: 5
Thanks: 0

Ah, that makes sense. Thanks again! I was studying for a college final and just took it this morning. I feel like I did really well on it!
itiffanysphone is offline  
December 10th, 2014, 08:13 AM   #7
Senior Member
 
Joined: Apr 2014
From: Glasgow

Posts: 2,157
Thanks: 732

Math Focus: Physics, mathematical modelling, numerical and computational solutions
Nice one
Benit13 is offline  
Reply

  My Math Forum > High School Math Forum > Algebra

Tags
inequality, problem



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Problem about inequality dsrivera Algebra 4 November 26th, 2013 05:37 PM
Inequality problem Moth Algebra 2 September 14th, 2011 07:10 AM
Inequality problem Havoc Math Events 2 October 26th, 2010 08:15 AM
Problem with inequality Havoc Number Theory 1 October 25th, 2010 06:32 PM
Inequality Problem 012anonymousxyz Abstract Algebra 2 December 31st, 1969 04:00 PM





Copyright © 2019 My Math Forum. All rights reserved.