My Math Forum  

Go Back   My Math Forum > High School Math Forum > Pre-Calculus

Pre-Calculus Pre-Calculus Math Forum


Reply
 
LinkBack Thread Tools Display Modes
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 .
Attached Images
File Type: jpg 99C473E2-B609-4487-911E-A4C315125238.jpg (20.2 KB, 32 views)
Sususailor is offline  
 
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 y-axis.

Clear now?
JeffM1 is offline  
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.
Country Boy is offline  
April 28th, 2018, 01:42 PM   #4
Math Team
 
topsquark's Avatar
 
Joined: May 2013
From: The Astral plane

Posts: 1,797
Thanks: 715

Math Focus: Wibbly wobbly timey-wimey stuff.
Quote:
Originally Posted by Country Boy View Post
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 09:33 PM.
topsquark is offline  
April 28th, 2018, 01:55 PM   #5
Math Team
 
Joined: Jul 2011
From: Texas

Posts: 2,755
Thanks: 1405

Attached Images
File Type: jpg inequality_region.jpg (26.2 KB, 1 views)
skeeter is offline  
Reply

  My Math Forum > High School Math Forum > Pre-Calculus

Tags
help or advice, question, require



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Hello, I am currently studying for an undergrad scholarship. I require some help. Aleramos Academic Guidance 3 May 22nd, 2016 05:12 AM
Does solving systems of differential equations require linear algebra? petermojer Differential Equations 1 July 1st, 2014 04:51 AM
I require your assistance with math! Algeria Academic Guidance 4 June 19th, 2014 08:32 AM
Need advice WickedJack New Users 3 October 22nd, 2011 04:54 PM
require a value of h such that sin(x) equals for x maximus101 Calculus 3 March 8th, 2011 10:51 AM





Copyright © 2018 My Math Forum. All rights reserved.