log0,5(4х-3)/( х+7)<0​

log 0,5 ((4x - 3)/(x + 7)) < log 0,5 (1)

-log 2 ((4x - 3)/(x + 7)) < -log 2 (1)

log 2 ((4x - 3)/(x + 7)) > log 2 (1)

(4x - 3)/(x + 7) > 1

(4x - 3 - x - 7)/(x + 7) > 0

(3x - 10)/(x + 7) > 0

(3x - 10)(x + 7) > 0

(3x - 10)(x + 7) = 0

x = 10/3 ; x = -7

(3x - 10)(x + 7) > 0

x € (-беск. ; -7) U (10/3 ; +беск.)