document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=251888>Question 251888</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Life expectancies at birth for men and women can be modeled by the following functions: <BR>\n" );
document.write( "w(x)= 0.126x+76.74<BR>\n" );
document.write( "M(x)= 0.126x+69.11 <BR>\n" );
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document.write( "W(x) represents the life expectancy of women and M(x) represents the life expectancy of men. The x represents the years since 1975. (x=0 corresponds to the year 1975, x=5 corresponds to 1980, and so on). <BR>\n" );
document.write( "this goes on until 2000<BR>\n" );
document.write( " x is the years since 1975. 1975 0 1985-5 1990-15 1995- 20 2000- 25<BR>\n" );
document.write( "I am not understanding this I also have to figure out on a slope is the life expectantcy of men or women increasing more rapidly. then I have to determine the birth years in a inequality where the men life expectancy are greater than women <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #183590 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=183590\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Since the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W%28x%29=0.126x%2B76.74 ALIGN=MIDDLE  ALT=\"W%28x%29=0.126x%2B76.74\"   DISABLED_style= \"max-width:90%; height:auto;\" > is in slope-intercept form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=mx%2Bb ALIGN=MIDDLE  ALT=\"y=mx%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" >, where 'm' is the slope and 'b' is the y-intercept, this means that the slope is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=0.126 ALIGN=MIDDLE  ALT=\"m=0.126\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Similarly, for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=M%28x%29=+0.126x%2B69.11 ALIGN=MIDDLE  ALT=\"M%28x%29=+0.126x%2B69.11\"   DISABLED_style= \"max-width:90%; height:auto;\" >, this equation is also in slope-intercept form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=mx%2Bb ALIGN=MIDDLE  ALT=\"y=mx%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the slope is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=0.126 ALIGN=MIDDLE  ALT=\"m=0.126\"   DISABLED_style= \"max-width:90%; height:auto;\" > as well. So the two slopes are equal.\r<BR>\n" );
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document.write( "What this means is that the life expectancies are both increasing at the same rate. \r<BR>\n" );
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document.write( "To find out which years men have a greater life expectancy than women, simply set M(x) (life expectancy of men) greater than W(x) (life expectancy of women) like this\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=M%28x%29%3EW%28x%29 ALIGN=MIDDLE  ALT=\"M%28x%29%3EW%28x%29\"   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=0.126x%2B69.11%3E0.126x%2B76.74 ALIGN=MIDDLE  ALT=\"0.126x%2B69.11%3E0.126x%2B76.74\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=M%28x%29=+0.126x%2B69.11 ALIGN=MIDDLE  ALT=\"M%28x%29=+0.126x%2B69.11\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W%28x%29=0.126x%2B76.74 ALIGN=MIDDLE  ALT=\"W%28x%29=0.126x%2B76.74\"   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=1000%280.126x%2B69.11%29%3E1000%280.126x%2B76.74%29 ALIGN=MIDDLE  ALT=\"1000%280.126x%2B69.11%29%3E1000%280.126x%2B76.74%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by 1000 to clear out the decimals.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=126x%2B69110%3E126x%2B76740 ALIGN=MIDDLE  ALT=\"126x%2B69110%3E126x%2B76740\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute and multiply.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=126x%3E126x%2B76740-69110 ALIGN=MIDDLE  ALT=\"126x%3E126x%2B76740-69110\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=69110 ALIGN=MIDDLE  ALT=\"69110\"   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=126x-126x%3E76740-69110 ALIGN=MIDDLE  ALT=\"126x-126x%3E76740-69110\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=126x ALIGN=MIDDLE  ALT=\"126x\"   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=0x%3E76740-69110 ALIGN=MIDDLE  ALT=\"0x%3E76740-69110\"   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=0x%3E7630 ALIGN=MIDDLE  ALT=\"0x%3E7630\"   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=0%3E7630 ALIGN=MIDDLE  ALT=\"0%3E7630\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify.\r<BR>\n" );
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document.write( "Since this inequality is NEVER true for any value of 'x', this means that the original inequality is also NEVER true.\r<BR>\n" );
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document.write( "Since there are no solutions to the original inequality, this means that the life expectancy of men will never exceed the life expectancy of women.\r<BR>\n" );
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document.write( "Note: I would make sure that you copied the problem down correctly (or ask if there are any typos). </SPAN>\n" );
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