document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1151628>Question 1151628</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello,\r<BR>\n" );
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document.write( "How do I know which type of interval notation to use to answer a question?\r<BR>\n" );
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document.write( "Whether is be ( , ), ( , ] or [ , ). Are their any other types of intervals I am missing?\r<BR>\n" );
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document.write( "Also when answering a question like this how do I know which number or infinity sign to put where? \r<BR>\n" );
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document.write( "For example....\r<BR>\n" );
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document.write( "3(11x+14)+7 is greater than 19+3x\r<BR>\n" );
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document.write( "I put (-oo,-1), but the correct answer was (-1,oo), and I did have that answer in at one point but it said that it was incorrect since I had it in the interval notation of (-1,oo] instead. So I had the right answer at one point just in the wrong interval notation so it was still wrong. \r<BR>\n" );
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document.write( "Thank you. <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #773441 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=773441\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "There are two endpoints, and for each endpoint, there are two symbols to choose from: Either square bracket or curved parenthesis.\r<BR>\n" );
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document.write( "This gives 2*2 = 4 different possible ways to write the endpoints<BR>\n" );
document.write( "(, ) or (, ] or [, ) or [, ]\r<BR>\n" );
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document.write( "The square bracket tells the reader \"include this endpoint as part of the interval\", and the curved parenthesis says the opposite (\"Do not include this value as part of the interval\").\r<BR>\n" );
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document.write( "Let's solve 3(11x+14)+7 > 19+3x\r<BR>\n" );
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document.write( "3(11x+14)+7 > 19+3x<BR>\n" );
document.write( "3(11x)+3(14)+7 > 19+3x ... distribute<BR>\n" );
document.write( "33x+42+7 > 19+3x<BR>\n" );
document.write( "33x+49 > 19+3x<BR>\n" );
document.write( "33x+49-3x > 19+3x-3x ... subtract 3x from both sides<BR>\n" );
document.write( "30x+49 > 19<BR>\n" );
document.write( "30x+49-49 > 19-49 ... subtract 49 from both sides<BR>\n" );
document.write( "30x > -30<BR>\n" );
document.write( "30x/30 > -30/30 ... divide both sides by 30 (see note below)<BR>\n" );
document.write( "x > -1\r<BR>\n" );
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document.write( "To write x > -1 in interval notation, we would write <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large {\color{red}{(-1, \infty)}}\"><BR>\n" );
document.write( "We use curved parenthesis for the -1 because we don't include x = -1 itself<BR>\n" );
document.write( "This is because x > -1 would turn into -1 > -1 which is false.<BR>\n" );
document.write( "We would include x = -1 if the inequality sign was \"greater than or equal to\". The \"or equal to\" portion allows us to include the endpoint.\r<BR>\n" );
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document.write( "We never ever include infinity for one simple reason: There's no way to get to infinity. Infinity is not a number but rather a concept of numbers just going on forever. The same applies to negative infinity as well. This is why endpoints dealing with plus or minus infinity always have curved parenthesis. \r<BR>\n" );
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document.write( "note: the inequality sign stays the same because we are dividing both sides by a positive number. If we divided both sides by a negative number, then the inequality sign would flip. I suspect this is probably what happened when you got the solution x < -1. <BR>\n" );
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