document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1206574>Question 1206574</A>: <I><SPAN STYLE=\"word-break: break-all;\">  |sqrt(x+3)-((7+x)/4)|<0.5<BR>\n" );
document.write( "How to solve this inequality? I get -2.07<x<1.9<BR>\n" );
document.write( "But according to the textbook, it is -2.6<x<8.6<BR>\n" );
document.write( "Please help<BR>\n" );
document.write( "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 #844142 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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/cgi-bin/show-face.mpl?user=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=844142\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28sqrt%28x%2B3%29-%287%2Bx%29%2F4%29%3C0.5 ALIGN=MIDDLE  ALT=\"abs%28sqrt%28x%2B3%29-%287%2Bx%29%2F4%29%3C0.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-0.5%3Csqrt%28x%2B3%29-%287%2Bx%29%2F4%3C0.5 ALIGN=MIDDLE  ALT=\"-0.5%3Csqrt%28x%2B3%29-%287%2Bx%29%2F4%3C0.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-0.5%3Csqrt%28x%2B3%29-%287%2Bx%29%2F4 ALIGN=MIDDLE  ALT=\"-0.5%3Csqrt%28x%2B3%29-%287%2Bx%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%2B3%29-%287%2Bx%29%2F4%3C0.5 ALIGN=MIDDLE  ALT=\"sqrt%28x%2B3%29-%287%2Bx%29%2F4%3C0.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "It turns out that the maximum value of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%2B3%29-%287%2Bx%29%2F4 ALIGN=MIDDLE  ALT=\"sqrt%28x%2B3%29-%287%2Bx%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > is 0, so we only need to solve the inequality <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-0.5%3Csqrt%28x%2B3%29-%287%2Bx%29%2F4%3C0 ALIGN=MIDDLE  ALT=\"-0.5%3Csqrt%28x%2B3%29-%287%2Bx%29%2F4%3C0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  If you try to solve the inequality <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%2B3%29-%287%2Bx%29%2F4%3C0.5 ALIGN=MIDDLE  ALT=\"sqrt%28x%2B3%29-%287%2Bx%29%2F4%3C0.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > you will find that there are no real solutions.<br><BR>\n" );
document.write( "Solve the corresponding EQUATION to find the endpoints of the solution interval.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-0.5=sqrt%28x%2B3%29-%287%2Bx%29%2F4 ALIGN=MIDDLE  ALT=\"-0.5=sqrt%28x%2B3%29-%287%2Bx%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Multiply everything by 4 to clear fractions<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2=4sqrt%28x%2B3%29-7-x ALIGN=MIDDLE  ALT=\"-2=4sqrt%28x%2B3%29-7-x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Isolate the term with the radical<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B5=4sqrt%28x%2B3%29 ALIGN=MIDDLE  ALT=\"x%2B5=4sqrt%28x%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Square both sides to eliminate the radical<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B10x%2B25=16x%2B48 ALIGN=MIDDLE  ALT=\"x%5E2%2B10x%2B25=16x%2B48\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-6x-23=0 ALIGN=MIDDLE  ALT=\"x%5E2-6x-23=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The quadratic does not factor; use the quadratic formula<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%286%2Bsqrt%2836%2B92%29%29%2F2 ALIGN=MIDDLE  ALT=\"x=%286%2Bsqrt%2836%2B92%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%286-sqrt%2836%2B92%29%29%2F2 ALIGN=MIDDLE  ALT=\"x=%286-sqrt%2836%2B92%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%286%2B8sqrt%282%29%29%2F2 ALIGN=MIDDLE  ALT=\"x=%286%2B8sqrt%282%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%286-8sqrt%282%29%29%2F2 ALIGN=MIDDLE  ALT=\"x=%286-8sqrt%282%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3%2B4sqrt%282%29 ALIGN=MIDDLE  ALT=\"x=3%2B4sqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3-4sqrt%282%29 ALIGN=MIDDLE  ALT=\"x=3-4sqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "To 3 decimal places, the solutions are -2.657 and 8.657.<br><BR>\n" );
document.write( "A graph....<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-10%2C10%2C-1%2C1%2C-0.5%2C0.5%2Cabs%28sqrt%28x%2B3%29-%287%2Bx%29%2F4%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );