Solve 5/2+6<4x+3/9

$$\frac { 5 } { 2 } + 6 < 4 x + \frac { 3 } { 9 }$$

Solve for x

$$x>\frac{49}{24}$$

Solution Steps

Convert 6 to fraction \frac{12}{2}.

$$\frac{5}{2}+\frac{12}{2}<4x+\frac{3}{9}$$

Since \frac{5}{2} and \frac{12}{2} have the same denominator, add them by adding their numerators.

$$\frac{5+12}{2}<4x+\frac{3}{9}$$

Add 5 and 12 to get 17.

$$\frac{17}{2}<4x+\frac{3}{9}$$

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

$$\frac{17}{2}<4x+\frac{1}{3}$$

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

$$4x+\frac{1}{3}>\frac{17}{2}$$

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

$$4x>\frac{17}{2}-\frac{1}{3}$$

Least common multiple of 2 and 3 is 6. Convert \frac{17}{2} and \frac{1}{3} to fractions with denominator 6.

$$4x>\frac{51}{6}-\frac{2}{6}$$

Since \frac{51}{6} and \frac{2}{6} have the same denominator, subtract them by subtracting their numerators.

$$4x>\frac{51-2}{6}$$

Subtract 2 from 51 to get 49.

$$4x>\frac{49}{6}$$

Divide both sides by 4. Since 4 is positive, the inequality direction remains the same.

$$x>\frac{\frac{49}{6}}{4}$$

Express \frac{\frac{49}{6}}{4} as a single fraction.

$$x>\frac{49}{6\times 4}$$

Multiply 6 and 4 to get 24.

$$x>\frac{49}{24}$$