Trigonometry Examples

$- \frac{π}{2} < 7 x + π < \frac{π}{2}$

Step 1

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

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Step 1.1

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

$- \frac{π}{2} - π < 7 x < \frac{π}{2} - π$

Step 1.2

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

$- \frac{π}{2} - π \cdot \frac{2}{2} < 7 x < \frac{π}{2} - π$

Step 1.3

Combine fractions.

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Step 1.3.1

Combine $- π$ and $\frac{2}{2}$ .

$- \frac{π}{2} + \frac{- π \cdot 2}{2} < 7 x < \frac{π}{2} - π$

Step 1.3.2

Combine the numerators over the common denominator.

$\frac{- π - π \cdot 2}{2} < 7 x < \frac{π}{2} - π$

Step 1.4

Simplify the numerator.

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Step 1.4.1

Multiply $2$ by $- 1$ .

$\frac{- π - 2 π}{2} < 7 x < \frac{π}{2} - π$

Step 1.4.2

Subtract $2 π$ from $- π$ .

$\frac{- 3 π}{2} < 7 x < \frac{π}{2} - π$

Step 1.5

Move the negative in front of the fraction.

$- \frac{3 π}{2} < 7 x < \frac{π}{2} - π$

Step 1.6

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

$- \frac{3 π}{2} < 7 x < \frac{π}{2} - π \cdot \frac{2}{2}$

Step 1.7

Combine fractions.

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Step 1.7.1

Combine $- π$ and $\frac{2}{2}$ .

$- \frac{3 π}{2} < 7 x < \frac{π}{2} + \frac{- π \cdot 2}{2}$

Step 1.7.2

Combine the numerators over the common denominator.

$- \frac{3 π}{2} < 7 x < \frac{π - π \cdot 2}{2}$

Step 1.8

Simplify the numerator.

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Step 1.8.1

Multiply $2$ by $- 1$ .

$- \frac{3 π}{2} < 7 x < \frac{π - 2 π}{2}$

Step 1.8.2

Subtract $2 π$ from $π$ .

$- \frac{3 π}{2} < 7 x < \frac{- π}{2}$

Step 1.9

Move the negative in front of the fraction.

$- \frac{3 π}{2} < 7 x < - \frac{π}{2}$

Step 2

Divide each term in the inequality by $7$ .

$\frac{- \frac{3 π}{2}}{7} < \frac{7 x}{7} < \frac{- \frac{π}{2}}{7}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$- \frac{3 π}{2} \cdot \frac{1}{7} < \frac{7 x}{7} < \frac{- \frac{π}{2}}{7}$

Step 4

Multiply $- \frac{3 π}{2} \cdot \frac{1}{7}$ .

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Step 4.1

Multiply $\frac{1}{7}$ by $\frac{3 π}{2}$ .

$- \frac{3 π}{7 \cdot 2} < \frac{7 x}{7} < \frac{- \frac{π}{2}}{7}$

Step 4.2

Multiply $7$ by $2$ .

$- \frac{3 π}{14} < \frac{7 x}{7} < \frac{- \frac{π}{2}}{7}$

Step 5

Cancel the common factor of $7$ .

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Step 5.1

Cancel the common factor.

$- \frac{3 π}{14} < \frac{7 x}{7} < \frac{- \frac{π}{2}}{7}$

Step 5.2

Divide $x$ by $1$ .

$- \frac{3 π}{14} < x < \frac{- \frac{π}{2}}{7}$

Step 6

Multiply the numerator by the reciprocal of the denominator.

$- \frac{3 π}{14} < x < - \frac{π}{2} \cdot \frac{1}{7}$

Step 7

Multiply $- \frac{π}{2} \cdot \frac{1}{7}$ .

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Step 7.1

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

$- \frac{3 π}{14} < x < - \frac{π}{7 \cdot 2}$

Step 7.2

Multiply $7$ by $2$ .

$- \frac{3 π}{14} < x < - \frac{π}{14}$

Step 8

Convert the inequality to interval notation.

$(- \frac{3 π}{14}, - \frac{π}{14})$

Step 9