document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=198548>Question 198548</A>: <I><SPAN STYLE=\"word-break: break-all;\"> solve:<BR>\n" );
document.write( "10^x+3>100^x-1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #149085 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=149085\">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=10%5E%28x%2B3%29%3E100%5E%28x-1%29 ALIGN=MIDDLE  ALT=\"10%5E%28x%2B3%29%3E100%5E%28x-1%29\"   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=10%5E%28x%2B3%29%3E%2810%5E2%29%5E%28x-1%29 ALIGN=MIDDLE  ALT=\"10%5E%28x%2B3%29%3E%2810%5E2%29%5E%28x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite 100 as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%5E2 ALIGN=MIDDLE  ALT=\"10%5E2\"   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=10%5E%28x%2B3%29%3E10%5E%282%28x-1%29%29 ALIGN=MIDDLE  ALT=\"10%5E%28x%2B3%29%3E10%5E%282%28x-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the exponents.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B3%3E2%28x-1%29 ALIGN=MIDDLE  ALT=\"x%2B3%3E2%28x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Since the bases are equal, this means that the right exponent MUST be larger than the left exponent.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B3%3E2x-2 ALIGN=MIDDLE  ALT=\"x%2B3%3E2x-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3E2x-2-3 ALIGN=MIDDLE  ALT=\"x%3E2x-2-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-2x%3E-2-3 ALIGN=MIDDLE  ALT=\"x-2x%3E-2-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x ALIGN=MIDDLE  ALT=\"2x\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x%3E-2-3 ALIGN=MIDDLE  ALT=\"-x%3E-2-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the left side.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x%3E-5 ALIGN=MIDDLE  ALT=\"-x%3E-5\"   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%28-5%29%2F%28-1%29 ALIGN=MIDDLE  ALT=\"x%3C%28-5%29%2F%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > to isolate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >. note: Remember, the inequality sign flips when we divide both sides by a negative number. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C5 ALIGN=MIDDLE  ALT=\"x%3C5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce.\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So the solution is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C5 ALIGN=MIDDLE  ALT=\"x%3C5\"   DISABLED_style= \"max-width:90%; height:auto;\" >  </SPAN>\n" );
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