Solve 5-2x/6<3/4

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

Solve for x

$$x>\frac{1}{4}$$

Solution Steps

Multiply both sides by 6. Since 6 is positive, the inequality direction remains the same.

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

Express \frac{3}{4}\times 6 as a single fraction.

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

Multiply 3 and 6 to get 18.

$$5-2x<\frac{18}{4}$$

Reduce the fraction \frac{18}{4} to lowest terms by extracting and canceling out 2.

$$5-2x<\frac{9}{2}$$

Subtract 5 from both sides.

$$-2x<\frac{9}{2}-5$$

Convert 5 to fraction \frac{10}{2}.

$$-2x<\frac{9}{2}-\frac{10}{2}$$

Since \frac{9}{2} and \frac{10}{2} have the same denominator, subtract them by subtracting their numerators.

$$-2x<\frac{9-10}{2}$$

Subtract 10 from 9 to get -1.

$$-2x<-\frac{1}{2}$$

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

$$x>\frac{-\frac{1}{2}}{-2}$$

Express \frac{-\frac{1}{2}}{-2} as a single fraction.

$$x>\frac{-1}{2\left(-2\right)}$$

Multiply 2 and -2 to get -4.

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

Fraction \frac{-1}{-4} can be simplified to \frac{1}{4} by removing the negative sign from both the numerator and the denominator.

$$x>\frac{1}{4}$$