document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=166106>Question 166106</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the following inequality and list solution in interval notation.\r<BR>\n" );
document.write( "\n" );
document.write( "|-3x-5|&#8805;10\r<BR>\n" );
document.write( "\n" );
document.write( "Can someone help me with this question, please. 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 #122389 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=122389\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28-3x-5%29%3E=10 ALIGN=MIDDLE  ALT=\"abs%28-3x-5%29%3E=10\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given inequality\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Break up the absolute value (remember, if you have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28x%29%3E=+a ALIGN=MIDDLE  ALT=\"abs%28x%29%3E=+a\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%3C=+-a ALIGN=MIDDLE  ALT=\"x+%3C=+-a\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%3E=+a ALIGN=MIDDLE  ALT=\"x+%3E=+a\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3x-5+%3C=+-10 ALIGN=MIDDLE  ALT=\"-3x-5+%3C=+-10\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3x-5+%3E=+10 ALIGN=MIDDLE  ALT=\"-3x-5+%3E=+10\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the absolute value inequality using the given rule\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now lets focus on the first inequality  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3x-5+%3C=+-10 ALIGN=MIDDLE  ALT=\"-3x-5+%3C=+-10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3x-5%3C=-10 ALIGN=MIDDLE  ALT=\"-3x-5%3C=-10\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given inequality\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3x%3C=-10%2B5 ALIGN=MIDDLE  ALT=\"-3x%3C=-10%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" >Add 5 to both sides\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3x%3C=-5 ALIGN=MIDDLE  ALT=\"-3x%3C=-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the right side\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3E=%28-5%29%2F%28-3%29 ALIGN=MIDDLE  ALT=\"x%3E=%28-5%29%2F%28-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by -3 to isolate x  (note: Remember, dividing both sides by a negative number flips the inequality sign) \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3E=5%2F3 ALIGN=MIDDLE  ALT=\"x%3E=5%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now lets focus on the second inequality  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3x-5+%3E=+10 ALIGN=MIDDLE  ALT=\"-3x-5+%3E=+10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3x-5%3E=10 ALIGN=MIDDLE  ALT=\"-3x-5%3E=10\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given inequality\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3x%3E=10%2B5 ALIGN=MIDDLE  ALT=\"-3x%3E=10%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" >Add 5 to both sides\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3x%3E=15 ALIGN=MIDDLE  ALT=\"-3x%3E=15\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the right side\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C=%2815%29%2F%28-3%29 ALIGN=MIDDLE  ALT=\"x%3C=%2815%29%2F%28-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by -3 to isolate x  (note: Remember, dividing both sides by a negative number flips the inequality sign) \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C=-5 ALIGN=MIDDLE  ALT=\"x%3C=-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "----------------------------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Answer:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So our answer is\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%3E=+5%2F3 ALIGN=MIDDLE  ALT=\"x+%3E=+5%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%3C=+-5 ALIGN=MIDDLE  ALT=\"x+%3C=+-5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So the solution in interval notation is: <font size=\"8\">(</font><IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \bf{-\infty,-5}\"><font size=\"8\">]</font> <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \cup\"><font size=\"8\">[</font><IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \bf{\frac{5}{3},\infty}\"><font size=\"8\">)</font>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So the solution in set builder notation is: <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left\{x\|x\le-5 \textrm{..or..} x\ge\frac{5}{3}\right\}\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Here's the graph of the solution set\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28500%2C80%2C-10%2C+6.66666666666667%2C-10%2C+10%2C%0D%0Anumber_line%28+500%2C+-10%2C+6.66666666666667+%2C-5%2C5%2F3%29%2C%0D%0A%0D%0Ablue%28arrow%28-5%2C0%2C-10%2C0%29%29%2C%0D%0Ablue%28arrow%28-5%2C0.30%2C-10%2C0.30%29%29%2C%0D%0Ablue%28arrow%28-5%2C0.15%2C-10%2C0.15%29%29%2C%0D%0Ablue%28arrow%28-5%2C-0.15%2C-10%2C-0.15%29%29%2C%0D%0Ablue%28arrow%28-5%2C-0.30%2C-10%2C-0.30%29%29%2C%0D%0A%0D%0A%0D%0Ablue%28arrow%285%2F3%2C0%2C6.66666666666667%2C0%29%29%2C%0D%0Ablue%28arrow%285%2F3%2C0.30%2C6.66666666666667%2C0.30%29%29%2C%0D%0Ablue%28arrow%285%2F3%2C0.15%2C6.66666666666667%2C0.15%29%29%2C%0D%0Ablue%28arrow%285%2F3%2C-0.15%2C6.66666666666667%2C-0.15%29%29%2C%0D%0Ablue%28arrow%285%2F3%2C-0.30%2C6.66666666666667%2C-0.30%29%29%0D%0A%0D%0A%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Note:\r<BR>\n" );
document.write( "\n" );
document.write( "There is a <b>closed</b> circle at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-5 ALIGN=MIDDLE  ALT=\"x=-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > which means that we're including that value from the solution set.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Also, there is a <b>closed</b> circle at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=5%2F3 ALIGN=MIDDLE  ALT=\"x=5%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > which means that we're including that value from the solution set.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );