Solve for x -pi/2<2x-pi<pi/2

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

Step 1

Move all terms not containing $x$ from the center section of the inequality.

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

$- \frac{π}{2} + π < 2 x < \frac{π}{2} + π$

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

$- \frac{π}{2} + π \cdot \frac{2}{2} < 2 x < \frac{π}{2} + π$

Combine fractions.

Combine $π$ and $\frac{2}{2}$ .

$- \frac{π}{2} + \frac{π \cdot 2}{2} < 2 x < \frac{π}{2} + π$

Combine the numerators over the common denominator.

$\frac{- π + π \cdot 2}{2} < 2 x < \frac{π}{2} + π$

Simplify the numerator.

Move $2$ to the left of $π$ .

$\frac{- π + 2 \cdot π}{2} < 2 x < \frac{π}{2} + π$

Add $- π$ and $2 π$ .

$\frac{π}{2} < 2 x < \frac{π}{2} + π$

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

$\frac{π}{2} < 2 x < \frac{π}{2} + π \cdot \frac{2}{2}$

Combine fractions.

Combine $π$ and $\frac{2}{2}$ .

$\frac{π}{2} < 2 x < \frac{π}{2} + \frac{π \cdot 2}{2}$

Combine the numerators over the common denominator.

$\frac{π}{2} < 2 x < \frac{π + π \cdot 2}{2}$

Simplify the numerator.

Move $2$ to the left of $π$ .

$\frac{π}{2} < 2 x < \frac{π + 2 \cdot π}{2}$

Add $π$ and $2 π$ .

$\frac{π}{2} < 2 x < \frac{3 π}{2}$

Step 2

Divide each term in the inequality by $2$ .

$\frac{\frac{π}{2}}{2} < \frac{2 x}{2} < \frac{\frac{3 π}{2}}{2}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$\frac{π}{2} \cdot \frac{1}{2} < \frac{2 x}{2} < \frac{\frac{3 π}{2}}{2}$

Step 4

Multiply $\frac{π}{2} \cdot \frac{1}{2}$ .

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

$\frac{π}{2 \cdot 2} < \frac{2 x}{2} < \frac{\frac{3 π}{2}}{2}$

Multiply $2$ by $2$ .

$\frac{π}{4} < \frac{2 x}{2} < \frac{\frac{3 π}{2}}{2}$

Step 5

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{π}{4} < \frac{2 x}{2} < \frac{\frac{3 π}{2}}{2}$

Divide $x$ by $1$ .

$\frac{π}{4} < x < \frac{\frac{3 π}{2}}{2}$

Step 6

Multiply the numerator by the reciprocal of the denominator.

$\frac{π}{4} < x < \frac{3 π}{2} \cdot \frac{1}{2}$

Step 7

Multiply $\frac{3 π}{2} \cdot \frac{1}{2}$ .

Multiply $\frac{3 π}{2}$ by $\frac{1}{2}$ .

$\frac{π}{4} < x < \frac{3 π}{2 \cdot 2}$

Multiply $2$ by $2$ .

$\frac{π}{4} < x < \frac{3 π}{4}$

Step 8

The result can be shown in multiple forms.

Inequality Form:

$\frac{π}{4} < x < \frac{3 π}{4}$

Interval Notation:

$(\frac{π}{4}, \frac{3 π}{4})$

Step 9

Solve for x -pi/2<2x-pi<pi/2

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