Solve 4X-5>8X+1/4

$$4 X - 5 > 8 X + 1 / 4$$

Solve for X

$$X<-\frac{21}{16}$$

Solution Steps

Subtract 8X from both sides.

$$4X-5-8X>\frac{1}{4}$$

Combine 4X and -8X to get -4X.

$$-4X-5>\frac{1}{4}$$

Add 5 to both sides.

$$-4X>\frac{1}{4}+5$$

Convert 5 to fraction \frac{20}{4}.

$$-4X>\frac{1}{4}+\frac{20}{4}$$

Since \frac{1}{4} and \frac{20}{4} have the same denominator, add them by adding their numerators.

$$-4X>\frac{1+20}{4}$$

Add 1 and 20 to get 21.

$$-4X>\frac{21}{4}$$

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

$$X<\frac{\frac{21}{4}}{-4}$$

Express \frac{\frac{21}{4}}{-4} as a single fraction.

$$X<\frac{21}{4\left(-4\right)}$$

Multiply 4 and -4 to get -16.

$$X<\frac{21}{-16}$$

Fraction \frac{21}{-16} can be rewritten as -\frac{21}{16} by extracting the negative sign.

$$X<-\frac{21}{16}$$