Solve the Inequality for x 9>x-2 1/4

$9 > x - 2 \frac{1}{4}$

Simplify the right side.

Convert $2 \frac{1}{4}$ to an improper fraction.

A mixed number is an addition of its whole and fractional parts.

$9 > x - (2 + \frac{1}{4})$

Add $2$ and $\frac{1}{4}$ .

To write $2$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$9 > x - (2 \cdot \frac{4}{4} + \frac{1}{4})$

Combine $2$ and $\frac{4}{4}$ .

$9 > x - (\frac{2 \cdot 4}{4} + \frac{1}{4})$

Combine the numerators over the common denominator.

$9 > x - \frac{2 \cdot 4 + 1}{4}$

Simplify the numerator.

Multiply $2$ by $4$ .

$9 > x - \frac{8 + 1}{4}$

Add $8$ and $1$ .

$9 > x - \frac{9}{4}$

Rewrite so $x$ is on the left side of the inequality.

$x - \frac{9}{4} < 9$

Move all terms not containing $x$ to the right side of the inequality.

Add $\frac{9}{4}$ to both sides of the inequality.

$x < 9 + \frac{9}{4}$

To write $9$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$x < 9 \cdot \frac{4}{4} + \frac{9}{4}$

Combine $9$ and $\frac{4}{4}$ .

$x < \frac{9 \cdot 4}{4} + \frac{9}{4}$

Combine the numerators over the common denominator.

$x < \frac{9 \cdot 4 + 9}{4}$

Simplify the numerator.

Multiply $9$ by $4$ .

$x < \frac{36 + 9}{4}$

Add $36$ and $9$ .

$x < \frac{45}{4}$

The result can be shown in multiple forms.

Inequality Form:

$x < \frac{45}{4}$

Interval Notation:

$(- \infty, \frac{45}{4})$