Solve x-3/4-2>x/3+1

$$\frac { x - 3 } { 4 } - 2 > \frac { x } { 3 } + 1$$

Solve for x

$$x<-45$$

Solution Steps

Multiply both sides of the equation by 12, the least common multiple of 4,3. Since 12 is positive, the inequality direction remains the same.

$$3\left(x-3\right)-24>4x+12$$

Use the distributive property to multiply 3 by x-3.

$$3x-9-24>4x+12$$

Subtract 24 from -9 to get -33.

$$3x-33>4x+12$$

Subtract 4x from both sides.

$$3x-33-4x>12$$

Combine 3x and -4x to get -x.

$$-x-33>12$$

Add 33 to both sides.

$$-x>12+33$$

Add 12 and 33 to get 45.

$$-x>45$$

Divide both sides by -1. Since -1 is negative, the inequality direction is changed.

$$x<-45$$