$$7\left(3-x\right)<4\left(2x-6\right)$$
Use the distributive property to multiply $7$ by $3-x$.$$21-7x<4\left(2x-6\right)$$
Use the distributive property to multiply $4$ by $2x-6$.$$21-7x<8x-24$$
Subtract $8x$ from both sides.$$21-7x-8x<-24$$
Combine $-7x$ and $-8x$ to get $-15x$.$$21-15x<-24$$
Subtract $21$ from both sides.$$-15x<-24-21$$
Subtract $21$ from $-24$ to get $-45$.$$-15x<-45$$
Divide both sides by $-15$. Since $-15$ is negative, the inequality direction is changed.$$x>\frac{-45}{-15}$$
Divide $-45$ by $-15$ to get $3$.$$x>3$$