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April 22nd, 2018, 04:32 PM  #1 
Newbie Joined: Apr 2018 From: Australia Posts: 1 Thanks: 0  Require some help/advice on this question
I’ve attached the question below. I would love for anyone to assist me thanks urgently .

April 22nd, 2018, 06:23 PM  #2 
Senior Member Joined: May 2016 From: USA Posts: 1,038 Thanks: 423 
Do you understand why they say to consider the corresponding equalities? If you say $x + y < 2$, then the region where that is true is everything under and to the left of the line $x + y = 2.$ If you say $x + y > 2$, then the region where that is true is everything over and to the right of the line $x + y = 2.$ Do you understand that? If so, all you need to do in this problem is to graph the equalities related to each inequality, determine what region is indicated by the inequality, and find the region where they all overlap. To get you started, the inequalities $x \ge 0 \text { and } y \ge 0$ have the corresponding equalities $x = 0 \text { and } y = 0$, namely the x and y axis, and the region indicated by the > is above the x axis and to the right of the yaxis. Clear now? 
April 28th, 2018, 11:16 AM  #3 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,194 Thanks: 871 
The first inequality is $\displaystyle 2x+ y\le 21$. As JeffM1 told you, that is bounded by the equality $\displaystyle 2x+ y= 21$. When x = 0, that becomes y = 21 so mark the point (0, 21). When y= 0, that becomes 2x = 21 so x = 21/2 = 10 and 1/2. Mark the point (21/2, 0). A line is determined by two points, so the graph of all (x, y) that satisfy 2x + y = 21. The set of all (x, 6) that satisfy $\displaystyle 2x+ y\le 21$ is that lie together with all points below and to the left (that set contains (0, 0), which obviously satisfies 2x + y < 21).
Last edited by skipjack; April 28th, 2018 at 09:30 PM. 
April 28th, 2018, 01:42 PM  #4  
Math Team Joined: May 2013 From: The Astral plane Posts: 1,797 Thanks: 715 Math Focus: Wibbly wobbly timeywimey stuff.  Quote:
Dan Last edited by skipjack; April 28th, 2018 at 09:33 PM.  
April 28th, 2018, 01:55 PM  #5 
Math Team Joined: Jul 2011 From: Texas Posts: 2,755 Thanks: 1405  

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