document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=134463>Question 134463</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I HOPE U CAN HELP ME WITH THIS....SOLVE THE EQUATION AND INEQUALITIES.  WRITE THE SOLUTION TO THE INEQUALITIES IN INTERVAL NOTATION.  THANK U.\r<BR>\n" );
document.write( "\n" );
document.write( "A) 2|3-P|-4=2\r<BR>\n" );
document.write( "\n" );
document.write( "B) 2|3-P|-4<2  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #98356 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=98356\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A) \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=2%2Aabs%283-p%29-4=2 ALIGN=MIDDLE  ALT=\"2%2Aabs%283-p%29-4=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation\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=2%2Aabs%283-p%29=6 ALIGN=MIDDLE  ALT=\"2%2Aabs%283-p%29=6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add 4 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=abs%283-p%29=3 ALIGN=MIDDLE  ALT=\"abs%283-p%29=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 2\r<BR>\n" );
document.write( "<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=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" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3-p=-3 ALIGN=MIDDLE  ALT=\"3-p=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3-p=3 ALIGN=MIDDLE  ALT=\"3-p=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Set the expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3-p ALIGN=MIDDLE  ALT=\"3-p\"   DISABLED_style= \"max-width:90%; height:auto;\" > equal to the original value 3 and it's opposite -3\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 equation  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3-p=-3 ALIGN=MIDDLE  ALT=\"3-p=-3\"   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=-p=-3-3 ALIGN=MIDDLE  ALT=\"-p=-3-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >Subtract 3 from 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=-p=-6 ALIGN=MIDDLE  ALT=\"-p=-6\"   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=p=%28-6%29%2F%28-1%29 ALIGN=MIDDLE  ALT=\"p=%28-6%29%2F%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by -1 to isolate p\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=p=6 ALIGN=MIDDLE  ALT=\"p=6\"   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( "<BR>\n" );
document.write( "\n" );
document.write( "<hr>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now lets focus on the second equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3-p=3 ALIGN=MIDDLE  ALT=\"3-p=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\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=-p=3-3 ALIGN=MIDDLE  ALT=\"-p=3-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >Subtract 3 from 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=-p=0 ALIGN=MIDDLE  ALT=\"-p=0\"   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=p=%280%29%2F%28-1%29 ALIGN=MIDDLE  ALT=\"p=%280%29%2F%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by -1 to isolate p\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=p=0 ALIGN=MIDDLE  ALT=\"p=0\"   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( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So the solutions to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Aabs%283-p%29-4=2 ALIGN=MIDDLE  ALT=\"2%2Aabs%283-p%29-4=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > are:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=6 ALIGN=MIDDLE  ALT=\"p=6\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=0 ALIGN=MIDDLE  ALT=\"p=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Notice if we graph  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2%2Aabs%283-x%29-4 ALIGN=MIDDLE  ALT=\"y=2%2Aabs%283-x%29-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2 ALIGN=MIDDLE  ALT=\"y=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > (just set each side equal to y and graph), we get\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=graph%28500%2C500%2C-2%2C8%2C-10%2C10%2C2%2Aabs%283-x%29-4%2C2%29 ALIGN=MIDDLE  ALT=\"graph%28500%2C500%2C-2%2C8%2C-10%2C10%2C2%2Aabs%283-x%29-4%2C2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2%2Aabs%283-x%29-4 ALIGN=MIDDLE  ALT=\"y=2%2Aabs%283-x%29-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > (red) and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2 ALIGN=MIDDLE  ALT=\"y=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >(green)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
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=0 ALIGN=MIDDLE  ALT=\"x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So this verifies our answer.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<hr>\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=2%2Aabs%283-p%29-4%3C2 ALIGN=MIDDLE  ALT=\"2%2Aabs%283-p%29-4%3C2\"   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=2%2Aabs%283-p%29%3C6 ALIGN=MIDDLE  ALT=\"2%2Aabs%283-p%29%3C6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add 4 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=abs%283-p%29%3C3 ALIGN=MIDDLE  ALT=\"abs%283-p%29%3C3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 2\r<BR>\n" );
document.write( "<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%3C+a ALIGN=MIDDLE  ALT=\"abs%28x%29%3C+a\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then <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;\" > and <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;\" >)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3-p+%3E+-3 ALIGN=MIDDLE  ALT=\"3-p+%3E+-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3-p+%3C+3 ALIGN=MIDDLE  ALT=\"3-p+%3C+3\"   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( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3+%3C+3-p+%3C+3 ALIGN=MIDDLE  ALT=\"-3+%3C+3-p+%3C+3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine the two inequalities to get a compound 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=-6+%3C+-p+%3C+0 ALIGN=MIDDLE  ALT=\"-6+%3C+-p+%3C+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 3 from all 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=6+%3E+p+%3E+0 ALIGN=MIDDLE  ALT=\"6+%3E+p+%3E+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply all sides by -1 to isolate p. This will flip the inequality signs\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%3Cp%3C6 ALIGN=MIDDLE  ALT=\"0%3Cp%3C6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rearrange the inequality\r<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=0%3Cp%3C6 ALIGN=MIDDLE  ALT=\"0%3Cp%3C6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "which looks like this in interval notation\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(0,6\right)\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "if you wanted to graph the solution set, you would get\r<BR>\n" );
document.write( "\n" );
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+-7%2C+13%29%2C%0D%0A%0D%0Ablue%28line%28-2.5%2C-7%2C2.65%2C-7%29%29%2C%0D%0Ablue%28line%28-2.5%2C-6%2C2.65%2C-6%29%29%2C%0D%0Ablue%28line%28-2.5%2C-5%2C2.65%2C-5%29%29%2C%0D%0A%0D%0Acircle%28-3%2C-5.8%2C0.35%29%2C%0D%0Acircle%28-3%2C-5.8%2C0.4%29%2C%0D%0Acircle%28-3%2C-5.8%2C0.45%29%2C%0D%0A%0D%0A%0D%0Acircle%283%2C-5.8%2C0.35%29%2C%0D%0Acircle%283%2C-5.8%2C0.4%29%2C%0D%0Acircle%283%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 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );