Solve 7(x+4)-⅔(x-6)≤2[x-3(x+5)]

Answer 1

7(x+4) - (2/3)(x-6) < 2(x-3(x+5))

7x + 28 -2x/3 - 4 < or + 2x- 6x -30

31x/3 < or = -6

x < or = -6(3/31) =- 18/31

x < or = -18/31

UNLESS you really meant to write

7(x+4) - 2/3(x-6) < or = 2(x-3(x+5))

7x +28 - 2/(3x-18) < or = 2(-2x -15) =-4x -30

11x +58 < or = 2/(3x-18)

(11x+58)(3x-18) < or = 2

33x^2 +174x - 198x - 1044 < or = 2

33xx^2 -24x - 1046 < or = 0

use the quadratic formula

x =24/66 + or - (1/66)sqr(24^2 -4(33)(-1046))

for the inequality part of the solution

it's as if the quadratic were factored, and both factors have to be the opposite sign to make the quadratic <0

but this is so tedious odds are you intended the 1st interpretation of the problem without a variable in the denominator.