Solve 5/2<55-x

$$\frac{ 5 }{ 2 } < 55-x$$

Solve for x

$$x<\frac{105}{2}$$

Solution Steps

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

$$55-x>\frac{5}{2}$$

Subtract 55 from both sides.

$$-x>\frac{5}{2}-55$$

Convert 55 to fraction \frac{110}{2}.

$$-x>\frac{5}{2}-\frac{110}{2}$$

Since \frac{5}{2} and \frac{110}{2} have the same denominator, subtract them by subtracting their numerators.

$$-x>\frac{5-110}{2}$$

Subtract 110 from 5 to get -105.

$$-x>-\frac{105}{2}$$

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

$$x<\frac{-\frac{105}{2}}{-1}$$

Express \frac{-\frac{105}{2}}{-1} as a single fraction.

$$x<\frac{-105}{2\left(-1\right)}$$

Multiply 2 and -1 to get -2.

$$x<\frac{-105}{-2}$$

Fraction \frac{-105}{-2} can be simplified to \frac{105}{2} by removing the negative sign from both the numerator and the denominator.

$$x<\frac{105}{2}$$