Algebra Examples

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

Step 1

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

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Subtract $π$ from 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.

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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.

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Multiply $2$ by $- 1$ .

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

Subtract $2 π$ from $- π$ .

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

Move the negative in front of the fraction.

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

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

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

Combine fractions.

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Combine $- π$ and $\frac{2}{2}$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

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Multiply $2$ by $- 1$ .

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

Subtract $2 π$ from $π$ .

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

Move the negative in front of the fraction.

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

Step 2

Divide each term in the inequality by $2$ .

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

Step 3

Multiply the numerator by the reciprocal of the denominator.

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

Step 4

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

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

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

Multiply $2$ by $2$ .

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

Step 5

Cancel the common factor of $2$ .

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Cancel the common factor.

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

Divide $x$ by $1$ .

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

Step 6

Multiply the numerator by the reciprocal of the denominator.

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

Step 7

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

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

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

Multiply $2$ by $2$ .

$- \frac{3 π}{4} < x < - \frac{π}{4}$

Step 8

The result can be shown in multiple forms.

Inequality Form:

$- \frac{3 π}{4} < x < - \frac{π}{4}$

Interval Notation:

$(- \frac{3 π}{4}, - \frac{π}{4})$

Step 9