Question 641087
{{{1/(b+4) <= 10+1/b}}}...I guess you have this

{{{1/(b+4) <= (10b+1)/b}}}...cross multiply

{{{1b <= (10b+1)(b+4)}}}

{{{b <= 10b^2+40b+b+4}}}

{{{0 <= 10b^2+40b+b-b+4}}}

{{{0 <= 10b^2+40b+4}}}


{{{0 <= 2(5b^2+20b+2)}}}....use quadratic formula and solve like equation


{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 


{{{x = (-20 +- sqrt( 20^2-4*5*2 ))/(2*5) }}} 


{{{x = (-20 +- sqrt( 400-40 ))/10 }}} 


{{{x = (-20 +- sqrt( 360 ))/10 }}} 


{{{x = (-20 +- 18.9)/10 }}} 


{{{x = (-20 +18.9)/10 }}} 

{{{x = -1.1/10 }}} 

{{{x = -0.11 }}} ....your {{{b}}}


{{{x = (-20 - 18.9)/10 }}} 

{{{x = -38.9/10 }}} 

{{{x = -3.89 }}} ....your {{{b}}}


check which one is right solution for {{{1/(b+4) <= 10+1/b}}}

{{{1/(-0.11+4) <= 10+1/-0.11}}}

{{{1/2.9 <= 10-9.09}}}

{{{0.34 <= 0.91}}}........true


{{{1/(-3.89+4) <= 10+1/-3.89}}}

{{{1/0.11 <= 10-0.26}}}

{{{9.09 <= 9.74}}}........true


{{{0.34 <= 0.91}}}........true