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April 22nd, 2018, 05:32 PM   #1
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Require some help/advice on this question

I’ve attached the question below. I would love for anyone to assist me thanks urgently .
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 April 22nd, 2018, 07:23 PM #2 Senior Member   Joined: May 2016 From: USA Posts: 1,210 Thanks: 498 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 y-axis. Clear now?
 April 28th, 2018, 12:16 PM #3 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,261 Thanks: 894 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 10:30 PM.
April 28th, 2018, 02:42 PM   #4
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Quote:
 Originally Posted by Country Boy 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).
Country Boy: The LaTeX here uses dollar sign and [math] tags.

-Dan

Last edited by skipjack; April 28th, 2018 at 10:33 PM.

April 28th, 2018, 02:55 PM   #5
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