Question

Помогите решить неравенство (2х-7)(3х+5) > (x+9)(6x-13)

Answer 1

$(2x-7)(3x+5) textgreater (x+9)(6x-13)$

$6x^2+10x-21x-35 textgreater 6x^2-13x+54x-117$

$6x^2-11x-35 textgreater 6x^2+41x-117$

$6x^2-11x-35-6x^2-41x+117 textgreater 0$

$-52x+82 textgreater 0$

$-52x textgreater -82$  

$26x textless 41$

$x textless frac{41}{26}$

$x textless 1 frac{15}{26}$

Ответ: $(-$∞$;1 frac{15}{26} )$