document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=262223>Question 262223</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I'm not sure what type of equation this is, but I need help on how the answer was found.  I am taking an SAT soon, and this is an example in my test booklet.  I don't know how they found the answers for these equations, can you please help me find out how to find the answer on my own?\r<BR>\n" );
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document.write( "Question:<BR>\n" );
document.write( "What value of X satisfies both of the equations below?<BR>\n" );
document.write( "|4x-7|=5 and |3-8x|=1\r<BR>\n" );
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document.write( "Since |4x-7|=5, the value of 4x-7 is either 5 or -5.<BR>\n" );
document.write( "4x-7=5       4x-7=-5<BR>\n" );
document.write( "4x=12    Or  4x=2           <BR>\n" );
document.write( "x=3          x=1/2      \r<BR>\n" );
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document.write( "(I don't see how 4x=12, x=3, 4x=2, etc...)\r<BR>\n" );
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document.write( "Since |3-8x|=1, the value of 3-8x is either 1 or -1.<BR>\n" );
document.write( "3-8x=1       3-8x=-1<BR>\n" );
document.write( "8x=2     Or  8x=4            <BR>\n" );
document.write( "x=1/4        x=1/2              \r<BR>\n" );
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document.write( "(again, I don't know how they got the answers for<BR>\n" );
document.write( " the equations.)\r<BR>\n" );
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document.write( "The two values of x that satisfy the second equation are 1/4 and 1/2.  You are asked to find the value of x that satisfies BOTH equations.  That value is 1/2.  The answer can be entered in the grid as 1/2 or .5.\r<BR>\n" );
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document.write( "I would appreciate some help on how they found the answers for the equations because I have no idea how this was answered.<BR>\n" );
document.write( "         </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #193170 by </B><A HREF=/tutors/aboutme.mpl?userid=drk><B>drk(1908)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=drk><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=193170\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> What value of X satisfies both of the equations below?<BR>\n" );
document.write( "(i) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%284x-7%29=5 ALIGN=MIDDLE  ALT=\"abs%284x-7%29=5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(ii) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%283-8x%29=1 ALIGN=MIDDLE  ALT=\"abs%283-8x%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "here are my steps:<BR>\n" );
document.write( "set (i) = 5 and then -5. solve for x.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284x-7%29+=+5 ALIGN=MIDDLE  ALT=\"%284x-7%29+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "add 7 to both sides to get<BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x+=+12 ALIGN=MIDDLE  ALT=\"4x+=+12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "divide by 4 on both sides to get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+3 ALIGN=MIDDLE  ALT=\"x+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x-7+=+-5 ALIGN=MIDDLE  ALT=\"4x-7+=+-5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "add 7 to both sides to get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x+=+2 ALIGN=MIDDLE  ALT=\"4x+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "divide by 4 to get<BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+1%2F2 ALIGN=MIDDLE  ALT=\"x+=+1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---<BR>\n" );
document.write( "Now we look at  (ii).<BR>\n" );
document.write( "setting it = 1 or -1, solving for x, we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3-8x+=+1 ALIGN=MIDDLE  ALT=\"3-8x+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "subtract 3 from both sides to get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-8x+=+-2 ALIGN=MIDDLE  ALT=\"-8x+=+-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "divide by -8 to get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+1%2F4 ALIGN=MIDDLE  ALT=\"x+=+1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3-8x+=+-1 ALIGN=MIDDLE  ALT=\"3-8x+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "subtract 3 from both sides to get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-8x+=+-4 ALIGN=MIDDLE  ALT=\"-8x+=+-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "divide by -8 to get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+1%2F2 ALIGN=MIDDLE  ALT=\"x+=+1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--<BR>\n" );
document.write( "Now looking at our answers we see that x = 1/2 is the same. So it is the answer we need. </SPAN>\n" );
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