Solve x-1/5+2<x/3

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

Solve for x

$$x>\frac{27}{2}$$

Solution Steps

Multiply both sides of the equation by 15, the least common multiple of 5,3. Since 15 is positive, the inequality direction remains the same.

$$3\left(x-1\right)+30<5x$$

Use the distributive property to multiply 3 by x-1.

$$3x-3+30<5x$$

Add -3 and 30 to get 27.

$$3x+27<5x$$

Subtract 5x from both sides.

$$3x+27-5x<0$$

Combine 3x and -5x to get -2x.

$$-2x+27<0$$

Subtract 27 from both sides. Anything subtracted from zero gives its negation.

$$-2x<-27$$

Divide both sides by -2. Since -2 is negative, the inequality direction is changed.

$$x>\frac{-27}{-2}$$

Fraction \frac{-27}{-2} can be simplified to \frac{27}{2} by removing the negative sign from both the numerator and the denominator.

$$x>\frac{27}{2}$$