document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=107469>Question 107469</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am having problems absolute value solving inequalities. I have two problems. I think I solved them, but I am not 100% sure. <BR>\n" );
document.write( "|5x+6|>26\r<BR>\n" );
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document.write( "x| x<-4 or x>4\r<BR>\n" );
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document.write( "the second problem is:\r<BR>\n" );
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document.write( "|2x-4| =16\r<BR>\n" );
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document.write( "x= -6 and 10 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #78255 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=78255\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> #1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%285x%2B6%29%3E26 ALIGN=MIDDLE  ALT=\"abs%285x%2B6%29%3E26\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given inequality\r<BR>\n" );
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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" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%2B6+%3C+-26 ALIGN=MIDDLE  ALT=\"5x%2B6+%3C+-26\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%2B6+%3E+26 ALIGN=MIDDLE  ALT=\"5x%2B6+%3E+26\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the absolute value inequality using the given rule\r<BR>\n" );
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document.write( "Now lets focus on the first inequality  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%2B6+%3C+-26 ALIGN=MIDDLE  ALT=\"5x%2B6+%3C+-26\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%2B6%3C-26 ALIGN=MIDDLE  ALT=\"5x%2B6%3C-26\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given inequality\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%3C-26-6 ALIGN=MIDDLE  ALT=\"5x%3C-26-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >Subtract 6 from both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%3C-32 ALIGN=MIDDLE  ALT=\"5x%3C-32\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the right side\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C%28-32%29%2F%285%29 ALIGN=MIDDLE  ALT=\"x%3C%28-32%29%2F%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 5 to isolate x \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C-32%2F5 ALIGN=MIDDLE  ALT=\"x%3C-32%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce\r<BR>\n" );
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document.write( "Now lets focus on the second inequality  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%2B6+%3E+26 ALIGN=MIDDLE  ALT=\"5x%2B6+%3E+26\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%2B6%3E26 ALIGN=MIDDLE  ALT=\"5x%2B6%3E26\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given inequality\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%3E26-6 ALIGN=MIDDLE  ALT=\"5x%3E26-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >Subtract 6 from both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%3E20 ALIGN=MIDDLE  ALT=\"5x%3E20\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the right side\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3E%2820%29%2F%285%29 ALIGN=MIDDLE  ALT=\"x%3E%2820%29%2F%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 5 to isolate x \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3E4 ALIGN=MIDDLE  ALT=\"x%3E4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So our answer is\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%3C+-32%2F5 ALIGN=MIDDLE  ALT=\"x+%3C+-32%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%3E+4 ALIGN=MIDDLE  ALT=\"x+%3E+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "which looks like this in interval notation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(-\infty,\frac{-32}{5}\right)\cup\left(4,\infty\right)\">\r<BR>\n" );
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document.write( "if you wanted to graph the solution set, you would get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28500%2C50%2C-10%2C10%2C-10%2C10%2C%0D%0Anumber_line%28+500%2C+-11.2%2C+8.8%29%2C%0D%0A%0D%0Ablue%28arrow%28-5.7%2C-7%2C-10%2C-7%29%29%2C%0D%0Ablue%28arrow%28-5.7%2C-6.5%2C-10%2C-6.5%29%29%2C%0D%0Ablue%28arrow%28-5.7%2C-6%2C-10%2C-6%29%29%2C%0D%0Ablue%28arrow%28-5.7%2C-5.5%2C-10%2C-5.5%29%29%2C%0D%0Ablue%28arrow%28-5.7%2C-5%2C-10%2C-5%29%29%2C%0D%0Ablue%28arrow%285.7%2C-7%2C10%2C-7%29%29%2C%0D%0Ablue%28arrow%285.7%2C-6.5%2C10%2C-6.5%29%29%2C%0D%0Ablue%28arrow%285.7%2C-6%2C10%2C-6%29%29%2C%0D%0Ablue%28arrow%285.7%2C-5.5%2C10%2C-5.5%29%29%2C%0D%0Ablue%28arrow%285.7%2C-5%2C10%2C-5%29%29%2C%0D%0A%0D%0Acircle%28-5.2%2C-5.8%2C0.35%29%2C%0D%0Acircle%28-5.2%2C-5.8%2C0.4%29%2C%0D%0Acircle%28-5.2%2C-5.8%2C0.45%29%2C%0D%0A%0D%0A%0D%0Acircle%285.2%2C-5.8%2C0.35%29%2C%0D%0Acircle%285.2%2C-5.8%2C0.4%29%2C%0D%0Acircle%285.2%2C-5.8%2C0.45%29%0D%0A%0D%0A%0D%0A%0D%0A%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Graph of the solution set in blue and the excluded values represented by open circles\r<BR>\n" );
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document.write( "#2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%282x-4%29=16 ALIGN=MIDDLE  ALT=\"abs%282x-4%29=16\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation\r<BR>\n" );
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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=a ALIGN=MIDDLE  ALT=\"abs%28x%29=a\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-a ALIGN=MIDDLE  ALT=\"x=-a\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=a ALIGN=MIDDLE  ALT=\"x=a\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-4=-16 ALIGN=MIDDLE  ALT=\"2x-4=-16\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-4=16 ALIGN=MIDDLE  ALT=\"2x-4=16\"   DISABLED_style= \"max-width:90%; height:auto;\" > Set the expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-4 ALIGN=MIDDLE  ALT=\"2x-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > equal to the original value 16 and it's opposite -16\r<BR>\n" );
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document.write( "Now lets focus on the first equation  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-4=-16 ALIGN=MIDDLE  ALT=\"2x-4=-16\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-4=-16 ALIGN=MIDDLE  ALT=\"2x-4=-16\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x=-16%2B4 ALIGN=MIDDLE  ALT=\"2x=-16%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" >Add 4 to both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x=-12 ALIGN=MIDDLE  ALT=\"2x=-12\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the right side\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-12%29%2F%282%29 ALIGN=MIDDLE  ALT=\"x=%28-12%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 2 to isolate x\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-6 ALIGN=MIDDLE  ALT=\"x=-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So our answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-6 ALIGN=MIDDLE  ALT=\"x=-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Now lets focus on the second equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-4=16 ALIGN=MIDDLE  ALT=\"2x-4=16\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-4=16 ALIGN=MIDDLE  ALT=\"2x-4=16\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x=16%2B4 ALIGN=MIDDLE  ALT=\"2x=16%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" >Add 4 to both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x=20 ALIGN=MIDDLE  ALT=\"2x=20\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the right side\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%2820%29%2F%282%29 ALIGN=MIDDLE  ALT=\"x=%2820%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 2 to isolate x\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=10 ALIGN=MIDDLE  ALT=\"x=10\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So our answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=10 ALIGN=MIDDLE  ALT=\"x=10\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "So the solutions to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%282x-4%29=16 ALIGN=MIDDLE  ALT=\"abs%282x-4%29=16\"   DISABLED_style= \"max-width:90%; height:auto;\" > are:\r<BR>\n" );
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document.write( "Notice if we graph  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=abs%282x-4%29 ALIGN=MIDDLE  ALT=\"y=abs%282x-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=16 ALIGN=MIDDLE  ALT=\"y=16\"   DISABLED_style= \"max-width:90%; height:auto;\" > (just set each side equal to y and graph), we get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28500%2C500%2C-20%2C20%2C-2%2C20%2Cabs%282x-4%29%2C16%29 ALIGN=MIDDLE  ALT=\"graph%28500%2C500%2C-20%2C20%2C-2%2C20%2Cabs%282x-4%29%2C16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=abs%282x-4%29 ALIGN=MIDDLE  ALT=\"y=abs%282x-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (red) and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=16 ALIGN=MIDDLE  ALT=\"y=16\"   DISABLED_style= \"max-width:90%; height:auto;\" >(green)\r<BR>\n" );
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document.write( "and we can see the two graphs intersect at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-6 ALIGN=MIDDLE  ALT=\"x=-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=10 ALIGN=MIDDLE  ALT=\"x=10\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So this verifies our answer.\r<BR>\n" );
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