document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1092649>Question 1092649</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need a little help on my homework. I tried them all and I know some of them are right i just have a question on a few because if i can understand those problems the ones similar I can do. So we are learning about how to solve inequalities and graphing them on a number line. I started this one but need a little help finishing it.<BR>\n" );
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document.write( "/x/>x-1, and i need 2 inequalities. i have the first which is x>x-1 but i don't have the other one and is not quite such how to solve either one and my other one is <BR>\n" );
document.write( "7-/2x/>5, I have both the inequalities and answers (x>-6; x<6) i just don't know how to put on the third number line because my teacher said something about the union? <BR>\n" );
document.write( "Can you help? That would be appreciative?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #707282 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=707282\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=\"black\" face=\"times\" size=\"3\"><BR>\n" );
document.write( "Problem 1) Solve |x| > x-1\r<BR>\n" );
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document.write( "If |x| > x-1, then we have two cases:<BR>\n" );
document.write( "Case A: x > x-1<BR>\n" );
document.write( "OR<BR>\n" );
document.write( "Case B: -x > x-1\r<BR>\n" );
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document.write( "The difference between case A and case B is that negative out front the first 'x'.\r<BR>\n" );
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document.write( "Let's solve for x in each case\r<BR>\n" );
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document.write( "Case A:<BR>\n" );
document.write( "x > x-1<BR>\n" );
document.write( "x-x > x-1-x<BR>\n" );
document.write( "0x > 0x - 1<BR>\n" );
document.write( "0 > -1<BR>\n" );
document.write( "This is always true so we effectively have infinitely many solutions for this inequality. In other words, pick any number you want for x and plug it into the inequality. You will get a true result.\r<BR>\n" );
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document.write( "Case B:<BR>\n" );
document.write( "-x > x-1<BR>\n" );
document.write( "-x+x > x-1+x<BR>\n" );
document.write( "0x > 2x-1<BR>\n" );
document.write( "0 > 2x-1<BR>\n" );
document.write( "2x-1 < 0<BR>\n" );
document.write( "2x-1+1 < 0+1<BR>\n" );
document.write( "2x+0 < 1<BR>\n" );
document.write( "2x < 1<BR>\n" );
document.write( "2x/2 < 1/2<BR>\n" );
document.write( "x < 1/2<BR>\n" );
document.write( "x < 0.5<BR>\n" );
document.write( "So any value smaller than 1/2 or 0.5 will work as a solution for this inequality\r<BR>\n" );
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document.write( "So to recap, the two solutions are<BR>\n" );
document.write( "Case A ---> all real numbers<BR>\n" );
document.write( "Case B ---> any real number smaller than 0.5\r<BR>\n" );
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document.write( "Since we have the keyword \"or\" as part of the absolute value definition, this means we combine the two results to get the final answer to be \"the set of all real numbers\".\r<BR>\n" );
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document.write( "We can plug any number in for x, into |x| > x-1, and we'll get a true result. It doesn't matter what number you pick\r<BR>\n" );
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document.write( "To graph this, simply draw a number line and shade everything on the number line. This indicates you're including all real numbers.\r<BR>\n" );
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document.write( "Problem 2) Solve 7-|2x| > 5\r<BR>\n" );
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document.write( "7-|2x| > 5<BR>\n" );
document.write( "7-|2x|+|2x| > 5+|2x|<BR>\n" );
document.write( "7 > 5+|2x|<BR>\n" );
document.write( "7-5 > 5+|2x|-5<BR>\n" );
document.write( "2 > |2x|<BR>\n" );
document.write( "|2x| < 2<BR>\n" );
document.write( "-2 < 2x < 2<BR>\n" );
document.write( "-2/2 < 2x/2 < 2/2<BR>\n" );
document.write( "-1 < x < 1\r<BR>\n" );
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document.write( "To graph this, draw a number line; then plot -1 and 1. Make sure there are open circles at -1 and 1. Finally shade between the open circles (don't shade over the open circles). <BR>\n" );
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