Solve for x -pi/2<1/2x<pi/2

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

Step 1

Combine $\frac{1}{2}$ and $x$ .

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

Step 2

Multiply each term in the inequality by $2$ .

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

Step 3

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{π}{2}$ into the numerator.

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 4

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

$- π < x < \frac{π}{2} \cdot 2$

Step 5

Cancel the common factor of $2$ .

Cancel the common factor.

$- π < x < \frac{π}{2} \cdot 2$

Rewrite the expression.

$- π < x < π$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$- π < x < π$

Interval Notation:

$(- π, π)$

Step 7