Evaluate: /(3-x) 4 < /(2 x-6) 7

Expression: $$\frac { 3 - x } { 4 } \lt \frac { 2 x - 6 } { 7 }$$

Multiply both sides of the equation by $28$, the least common multiple of $4,7$. Since $28$ is positive, the inequality direction remains the same.

$$7\left(3-x\right)<4\left(2x-6\right)$$

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 $3$.

$$x>3$$