Solve 2x-1/6-x-4/5<x/3

$$\frac { 2 x - 1 } { 6 } - \frac { x - 4 } { 5 } < \frac { x } { 3 }$$

Solve for x

$$x>\frac{19}{6}$$

Solution Steps

Multiply both sides of the equation by 30, the least common multiple of 6,5,3. Since 30 is positive, the inequality direction remains the same.

$$5\left(2x-1\right)-6\left(x-4\right)<10x$$

Use the distributive property to multiply 5 by 2x-1.

$$10x-5-6\left(x-4\right)<10x$$

Use the distributive property to multiply -6 by x-4.

$$10x-5-6x+24<10x$$

Combine 10x and -6x to get 4x.

$$4x-5+24<10x$$

Add -5 and 24 to get 19.

$$4x+19<10x$$

Subtract 10x from both sides.

$$4x+19-10x<0$$

Combine 4x and -10x to get -6x.

$$-6x+19<0$$

Subtract 19 from both sides. Anything subtracted from zero gives its negation.

$$-6x<-19$$

Divide both sides by -6. Since -6 is negative, the inequality direction is changed.

$$x>\frac{-19}{-6}$$

Fraction \frac{-19}{-6} can be simplified to \frac{19}{6} by removing the negative sign from both the numerator and the denominator.

$$x>\frac{19}{6}$$