Question 251888
Since the equation {{{W(x)=0.126x+76.74}}} is in slope-intercept form {{{y=mx+b}}}, where 'm' is the slope and 'b' is the y-intercept, this means that the slope is {{{m=0.126}}}.



Similarly, for {{{M(x)= 0.126x+69.11}}}, this equation is also in slope-intercept form {{{y=mx+b}}} and the slope is {{{m=0.126}}} as well. So the two slopes are equal.



What this means is that the life expectancies are both increasing at the same rate. 



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



{{{M(x)>W(x)}}}



{{{0.126x+69.11>0.126x+76.74}}} Plug in {{{M(x)= 0.126x+69.11}}} and {{{W(x)=0.126x+76.74}}}



{{{1000(0.126x+69.11)>1000(0.126x+76.74)}}} Multiply both sides by 1000 to clear out the decimals.



{{{126x+69110>126x+76740}}} Distribute and multiply.



{{{126x>126x+76740-69110}}} Subtract {{{69110}}} from both sides.



{{{126x-126x>76740-69110}}} Subtract {{{126x}}} from both sides.



{{{0x>76740-69110}}} Combine like terms on the left side.



{{{0x>7630}}} Combine like terms on the right side.



{{{0>7630}}} Simplify.



Since this inequality is NEVER true for any value of 'x', this means that the original inequality is also NEVER true.



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.



Note: I would make sure that you copied the problem down correctly (or ask if there are any typos).