Solve 3x-7/4<2x-1/8

$$\frac { 3 x - 7 } { 4 } < \frac { 2 x - 1 } { 8 }$$

Solve for x

$$x<\frac{13}{4}$$

Solution Steps

Multiply both sides of the equation by 8, the least common multiple of 4,8. Since 8 is positive, the inequality direction remains the same.

$$2\left(3x-7\right)<2x-1$$

Use the distributive property to multiply 2 by 3x-7.

$$6x-14<2x-1$$

Subtract 2x from both sides.

$$6x-14-2x<-1$$

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

$$4x-14<-1$$

Add 14 to both sides.

$$4x<-1+14$$

Add -1 and 14 to get 13.

$$4x<13$$

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

$$x<\frac{13}{4}$$