Solve 5-x/2<2/3

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

Solve for x

$$x>\frac{11}{3}$$

Solution Steps

Multiply both sides by 2. Since 2 is positive, the inequality direction remains the same.

$$5-x<\frac{2}{3}\times 2$$

Express \frac{2}{3}\times 2 as a single fraction.

$$5-x<\frac{2\times 2}{3}$$

Multiply 2 and 2 to get 4.

$$5-x<\frac{4}{3}$$

Subtract 5 from both sides.

$$-x<\frac{4}{3}-5$$

Convert 5 to fraction \frac{15}{3}.

$$-x<\frac{4}{3}-\frac{15}{3}$$

Since \frac{4}{3} and \frac{15}{3} have the same denominator, subtract them by subtracting their numerators.

$$-x<\frac{4-15}{3}$$

Subtract 15 from 4 to get -11.

$$-x<-\frac{11}{3}$$

Divide both sides by -1. Since -1 is negative, the inequality direction is changed.

$$x>\frac{-\frac{11}{3}}{-1}$$

Express \frac{-\frac{11}{3}}{-1} as a single fraction.

$$x>\frac{-11}{3\left(-1\right)}$$

Multiply 3 and -1 to get -3.

$$x>\frac{-11}{-3}$$

Fraction \frac{-11}{-3} can be simplified to \frac{11}{3} by removing the negative sign from both the numerator and the denominator.

$$x>\frac{11}{3}$$