Solve -4x+2/5>5/10?

$$- 4 x + \frac { 2 } { 5 } > \frac { 5 } { 10 } ?$$

Solve for x

$$x<-\frac{1}{40}$$

Solution Steps

Reduce the fraction \frac{5}{10} to lowest terms by extracting and canceling out 5.

$$-4x+\frac{2}{5}>\frac{1}{2}$$

Subtract \frac{2}{5} from both sides.

$$-4x>\frac{1}{2}-\frac{2}{5}$$

Least common multiple of 2 and 5 is 10. Convert \frac{1}{2} and \frac{2}{5} to fractions with denominator 10.

$$-4x>\frac{5}{10}-\frac{4}{10}$$

Since \frac{5}{10} and \frac{4}{10} have the same denominator, subtract them by subtracting their numerators.

$$-4x>\frac{5-4}{10}$$

Subtract 4 from 5 to get 1.

$$-4x>\frac{1}{10}$$

Divide both sides by -4. Since -4 is negative, the inequality direction is changed.

$$x<\frac{\frac{1}{10}}{-4}$$

Express \frac{\frac{1}{10}}{-4} as a single fraction.

$$x<\frac{1}{10\left(-4\right)}$$

Multiply 10 and -4 to get -40.

$$x<\frac{1}{-40}$$

Fraction \frac{1}{-40} can be rewritten as -\frac{1}{40} by extracting the negative sign.

$$x<-\frac{1}{40}$$