My Math Forum Inequality problem

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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: 7,958 Thanks: 1146 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: 7,958 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 $\displaystyle x\in(-\infty,-2]\cup[6,\infty)$
 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: 20,927 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.
 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: 2,157 Thanks: 732 Math Focus: Physics, mathematical modelling, numerical and computational solutions Nice one

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