document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1208860>Question 1208860</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the inequality. Express your answer using set notation and interval notation.  Graph the solution set.\r<BR>\n" );
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document.write( "(2x - 1)^(-1) > 0\r<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 #847355 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</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=847355\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "(2x-1)^(-1) is the same as 1/(2x-1)\r<BR>\n" );
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document.write( "As mentioned by the other tutor, 1/(2x-1) is positive if and only if 2x-1 > 0.<BR>\n" );
document.write( "That solves to x > 1/2\r<BR>\n" );
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document.write( "A visual way to demonstrate this is to use a graphing tool like <a  rel=nofollow HREF=\"https://www.geogebra.org/calculator\">GeoGebra</a> or <a  rel=nofollow HREF=\"https://www.desmos.com/calculator\">Desmos</a> to plot the graph of  y = 1/(2x-1)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0Adrawing%28500%2C500%2C-5%2C5%2C-5%2C5%2C%0D%0Agraph%28500%2C500%2C-5%2C5%2C-5%2C5%2C-100%2C1%2F%282x-1%29%29%2C%0D%0Aline%280.5%2C-6%2C0.5%2C-5.4%29%2Cline%280.5%2C-4.8%2C0.5%2C-4.2%29%2Cline%280.5%2C-3.6%2C0.5%2C-3%29%2Cline%280.5%2C-2.4%2C0.5%2C-1.8%29%2Cline%280.5%2C-1.2%2C0.5%2C-0.6%29%2Cline%280.5%2C0%2C0.5%2C0.6%29%2Cline%280.5%2C1.2%2C0.5%2C1.8%29%2Cline%280.5%2C2.4%2C0.5%2C3%29%2Cline%280.5%2C3.6%2C0.5%2C4.2%29%2Cline%280.5%2C4.8%2C0.5%2C5.4%29%0D%0A%29%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The vertical asymptote is x = 1/2 since this x value makes the denominator 2x-1 to be zero. Recall that dividing by zero is not allowed.\r<BR>\n" );
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document.write( "The portion of the curve to the right of x = 1/2 is entirely above the x axis. <BR>\n" );
document.write( "So we visually demonstrate the answer as an inequality is x > 1/2<BR>\n" );
document.write( "You can verify this using a table of values. \r<BR>\n" );
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document.write( "The answer in interval notation is (1/2, infinity)<BR>\n" );
document.write( "Replace the word \"infinity\" with the symbol if needed.\r<BR>\n" );
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document.write( "The graph on a number line will involve an open hole at 1/2 and shading to the right. The open hole indicates \"do not include this endpoint\".<BR>\n" );
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