Solve 25/2-1/4<x+1/3

$$\frac { 25 } { 2 } - \frac { 1 } { 4 } < x + \frac { 1 } { 3 }$$

Solve for x

$$x>\frac{143}{12}$$

Solution Steps

Least common multiple of 2 and 4 is 4. Convert \frac{25}{2} and \frac{1}{4} to fractions with denominator 4.

$$\frac{50}{4}-\frac{1}{4}<x+\frac{1}{3}$$

Since \frac{50}{4} and \frac{1}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{50-1}{4}<x+\frac{1}{3}$$

Subtract 1 from 50 to get 49.

$$\frac{49}{4}<x+\frac{1}{3}$$

Swap sides so that all variable terms are on the left hand side. This changes the sign direction.

$$x+\frac{1}{3}>\frac{49}{4}$$

Subtract \frac{1}{3} from both sides.

$$x>\frac{49}{4}-\frac{1}{3}$$

Least common multiple of 4 and 3 is 12. Convert \frac{49}{4} and \frac{1}{3} to fractions with denominator 12.

$$x>\frac{147}{12}-\frac{4}{12}$$

Since \frac{147}{12} and \frac{4}{12} have the same denominator, subtract them by subtracting their numerators.

$$x>\frac{147-4}{12}$$

Subtract 4 from 147 to get 143.

$$x>\frac{143}{12}$$