Solve x-2/4<x-1/3

$$\frac{ x-2 }{ 4 } < \frac{ x-1 }{ 3 }$$

Solve for x

$$x>-2$$

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.

$$3\left(x-2\right)<4\left(x-1\right)$$

Use the distributive property to multiply 3 by x-2.

$$3x-6<4\left(x-1\right)$$

Use the distributive property to multiply 4 by x-1.

$$3x-6<4x-4$$

Subtract 4x from both sides.

$$3x-6-4x<-4$$

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

$$-x-6<-4$$

Add 6 to both sides.

$$-x<-4+6$$

Add -4 and 6 to get 2.

$$-x<2$$

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

$$x>-2$$