document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1172851>Question 1172851</A>: <I><SPAN STYLE=\"word-break: break-all;\"> in compound inequalities, say you were given a disjunction inequality that read: -y +5 ≥ 9 or 3y + 4 < -5.  when solved, you’d get: y ≤ -4 or y < -3.  why would you only write one of the inequalities as your final answer, rather than one since it’s connected by, “or”?  as with a conjunction inequality, if they gave you for example, k > 1 and k > 5 (both signs are facing the same direction), why would you only write one of the inequalities?  if there’s a rule that corresponds with this, please tell me.  what/when does the rule apply to (if any)?  does this only happen in conjunction inequalities if both signs are facing the same direction and one of the inequalities can “fit” under the other?  fit meaning that (referring back to the previous example) all numbers greater than 1 aren’t all greater than 0, but all numbers greater than 5 are greater than 1?  please respond.  i have a math test on this soon, thank you 😄 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #797984 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3820)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=797984\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Using a number line may help visualize what's going on.\r<BR>\n" );
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document.write( "Graph y ≤ -4 by plotting a closed circle at -4 on the number line and then shade to the left. This indicates \"y is -4 or smaller\". \r<BR>\n" );
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document.write( "To graph y < -3, we will plot an open circle at -3 and shade to the left. The open circle says \"do not include this value as part of the solution set\". \r<BR>\n" );
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document.write( "Since we're combining those inequalities with the \"or\" keyword, this means we're looking for y values that are in either region. <BR>\n" );
document.write( "So either we're in region A which has y = -4 or smaller OR we're in region B which describes y values smaller than -3. \r<BR>\n" );
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document.write( "We can simplify those two regions to combine them to simply region B. <BR>\n" );
document.write( "As the diagram shows, if you are in region A (red), you're already in region B (blue), but not the other way around<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" width=\"50%\" src = \"https://i.imgur.com/RzfTOLs.png\">\r<BR>\n" );
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document.write( "Now for the next example:<BR>\n" );
document.write( "k > 1 and k > 5\r<BR>\n" );
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document.write( "To graph k > 1, we have an open hole at 1 and shading to the right to describe all values larger than 1. The value 1 is not part of the solution set.\r<BR>\n" );
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document.write( "The graph of k > 5 is similar, but the open hole is at 5 this time.\r<BR>\n" );
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document.write( "The keyword here is \"and\" this time. This means we need to be in BOTH regions at the same time. So we'll look where they overlap. The two regions overlap beyond 5. So that's why \"k > 1 and k > 5\" simplifies to \"k > 5\". \r<BR>\n" );
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document.write( "If you pick a number that's both larger than 1 AND larger than 5, then that number is larger than 5. This is because 5 is larger than 1.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" width=\"50%\" src = \"https://i.imgur.com/TGVeFvD.png\">\r<BR>\n" );
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document.write( "Hopefully these visual diagrams clear your question up. If not, then please let me know. <BR>\n" );
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