Solve 1-2x/3-5x-1/6>1

$$\frac{ 1-2x }{ 3 } - \frac{ 5x-1 }{ 6 } > 1$$

Solve for x

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

Solution Steps

Multiply both sides of the equation by 6, the least common multiple of 3,6. Since 6 is positive, the inequality direction remains the same.

$$2\left(1-2x\right)-\left(5x-1\right)>6$$

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

$$2-4x-\left(5x-1\right)>6$$

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

$$2-4x-5x-\left(-1\right)>6$$

The opposite of -1 is 1.

$$2-4x-5x+1>6$$

Combine -4x and -5x to get -9x.

$$2-9x+1>6$$

Add 2 and 1 to get 3.

$$3-9x>6$$

Subtract 3 from both sides.

$$-9x>6-3$$

Subtract 3 from 6 to get 3.

$$-9x>3$$

Divide both sides by -9. Since -9 is negative, the inequality direction is changed.

$$x<\frac{3}{-9}$$

Reduce the fraction \frac{3}{-9} to lowest terms by extracting and canceling out 3.

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