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

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

Solve for x

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

Solution Steps

Multiply both sides of the equation by 4, the least common multiple of 2,4. Since 4 is positive, the inequality direction remains the same.

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

Use the distributive property to multiply 2 by 3x+1.

$$6x+2<2x-1$$

Subtract 2x from both sides.

$$6x+2-2x<-1$$

Combine 6x and -2x to get 4x.

$$4x+2<-1$$

Subtract 2 from both sides.

$$4x<-1-2$$

Subtract 2 from -1 to get -3.

$$4x<-3$$

Divide both sides by 4. Since 4 is positive, the inequality direction remains the same.

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