Finite Math Examples

$x - \frac{1}{7} > \frac{1}{2}$

Step 1

Add $\frac{1}{7}$ to both sides of the inequality.

$x > \frac{1}{2} + \frac{1}{7}$

Step 2

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$x > \frac{1}{2} \cdot \frac{7}{7} + \frac{1}{7}$

Step 3

To write $\frac{1}{7}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$x > \frac{1}{2} \cdot \frac{7}{7} + \frac{1}{7} \cdot \frac{2}{2}$

Step 4

Write each expression with a common denominator of $14$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 4.1

Multiply $\frac{1}{2}$ by $\frac{7}{7}$ .

$x > \frac{7}{2 \cdot 7} + \frac{1}{7} \cdot \frac{2}{2}$

Step 4.2

Multiply $2$ by $7$ .

$x > \frac{7}{14} + \frac{1}{7} \cdot \frac{2}{2}$

Step 4.3

Multiply $\frac{1}{7}$ by $\frac{2}{2}$ .

$x > \frac{7}{14} + \frac{2}{7 \cdot 2}$

Step 4.4

Multiply $7$ by $2$ .

$x > \frac{7}{14} + \frac{2}{14}$

Step 5

Combine the numerators over the common denominator.

$x > \frac{7 + 2}{14}$

Step 6

Add $7$ and $2$ .

$x > \frac{9}{14}$

Step 7

The result can be shown in multiple forms.

Inequality Form:

$x > \frac{9}{14}$

Interval Notation:

$(\frac{9}{14}, \infty)$