Proving Inequality: (6x^2 - 7sinx)/(3x+1) >1000

[nhrock3]

i have this question and solution

i have a similar question which i can't solve similarly

i need to prove
(6x^2 - 7sinx)/(3x+1) >1000 for x>m and x>0
(6x^2 - 7sinx)/(3x+1) >(6x^2 - 7)/(3x+1)

that as far as i could go

 

[╔(σ_σ)╝]

Keep making approximations

(6x^2 - 7sinx)/(3x+1) >(6x^2 - 7)/(3x+1) > (6x^2 - 7sinx)/(3x+1) >(6x^2 - 7)/(3x+3x)

(6x^2 - 7)/(3x+3x) = (6x^2 -7)/6x = x -7/(6x)

 

[nhrock3]

(6x^2 - 7sinx)/(3x+1) >(6x^2 - 7)/(3x+3x)=x-7/x
what now
?

 

[╔(σ_σ)╝]

(6x^2 - 7sinx)/(3x+1) >(6x^2 - 7)/(3x+3x)=x-7/x
what now
?

What do you mean "what now "? Are not capable of thinking for yourself ?

If you have something like

x - 7/x if x>M and M > 1008

then

x - 7/x > x -7 > 1008 -7 = 1001