Solve 2x-1/2-5x-1/4<0

$$\frac { 2 x - 1 } { 2 } - \frac { 5 x - 1 } { 4 } < 0$$

Solve for x

$$x>-1$$

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.

$$2\left(2x-1\right)-\left(5x-1\right)<0$$

Use the distributive property to multiply 2 by 2x-1.

$$4x-2-\left(5x-1\right)<0$$

To find the opposite of 5x-1, find the opposite of each term.

$$4x-2-5x-\left(-1\right)<0$$

The opposite of -1 is 1.

$$4x-2-5x+1<0$$

Combine 4x and -5x to get -x.

$$-x-2+1<0$$

Add -2 and 1 to get -1.

$$-x-1<0$$

Add 1 to both sides. Anything plus zero gives itself.

$$-x<1$$

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

$$x>-1$$