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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. 
December 9th, 2014, 08:35 AM  #2 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,932 Thanks: 1127 Math Focus: Elementary mathematics and beyond  itiffanysphone, please post separate questions in their own thread. This helps to keep things organized.

December 9th, 2014, 09:34 AM  #3 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,932 Thanks: 1127 Math Focus: Elementary mathematics and beyond 
$\displaystyle 3+\left1\frac{x}{2}\right\ge5$ $\displaystyle \left1\frac{x}{2}\right\ge2$ $\displaystyle \left\frac{2x}{2}\right\ge2$ $\displaystyle \frac{2x}{2}\ge2$ $\displaystyle 2x\ge4$ Case 1: 2  x is positive, so 2  x = 2  x: $\displaystyle 2x\ge4$ $\displaystyle x\ge2$ $\displaystyle x\le2$ Case 2: 2  x is negative, so 2  x = x  2: $\displaystyle x2\ge4$ $\displaystyle x\ge6$ So we have $\displaystyle x\in(\infty,2]\cup[6,\infty)$ 
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? 
December 9th, 2014, 11:46 AM  #5 
Global Moderator Joined: Dec 2006 Posts: 20,484 Thanks: 2041 
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.

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!

December 10th, 2014, 08:13 AM  #7 
Senior Member Joined: Apr 2014 From: Glasgow Posts: 2,150 Thanks: 730 Math Focus: Physics, mathematical modelling, numerical and computational solutions 
Nice one 

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