Answer:
[tex]\large\boxed{x>-\dfrac{11}{24}}[/tex]
Step-by-step explanation:
[tex]-\dfrac{4}{3}x+\dfrac{1}{6}<\dfrac{7}{9}\qquad\text{multiply by common denominator}\to18\\\\18\!\!\!\!\!\diagup^6\left(-\dfrac{4}{3\!\!\!\!\diagup_1}x\right)+18\!\!\!\!\!\diagup^3\left(\dfrac{1}{6\!\!\!\!\diagup_1}\right)<18\!\!\!\!\!\diagup^2\left(\dfrac{7}{9\!\!\!\!\diagup_1}\right)\\\\(6)(-4x)+(3)(1)<(2)(7)\\\\-24x+3<14\qquad\text{subtract 3 from both sides}\\\\-24x<11\qquad\text{change the signs}\\\\24x>-11\qquad\text{divide both sides by 24}\\\\x>-\dfrac{11}{24}[/tex]
