Solve for x 0<x-pi/3<pi

$0 < x - \frac{π}{3} < π$

Step 1

Add $\frac{π}{3}$ to each section of the inequality because it does not contain the variable we are trying to solve for.

$0 + \frac{π}{3} < x < π + \frac{π}{3}$

Step 2

Add $0$ and $\frac{π}{3}$ .

$\frac{π}{3} < x < π + \frac{π}{3}$

Step 3

To write $π$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{π}{3} < x < π \cdot \frac{3}{3} + \frac{π}{3}$

Step 4

Combine fractions.

Combine $π$ and $\frac{3}{3}$ .

$\frac{π}{3} < x < \frac{π \cdot 3}{3} + \frac{π}{3}$

Combine the numerators over the common denominator.

$\frac{π}{3} < x < \frac{π \cdot 3 + π}{3}$

Step 5

Simplify the numerator.

Move $3$ to the left of $π$ .

$\frac{π}{3} < x < \frac{3 \cdot π + π}{3}$

Add $3 π$ and $π$ .

$\frac{π}{3} < x < \frac{4 π}{3}$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$\frac{π}{3} < x < \frac{4 π}{3}$

Interval Notation:

$(\frac{π}{3}, \frac{4 π}{3})$

Step 7