What is -pi/2 <x+pi/6 < pi/2 ?

The solution to -pi/2 <x+pi/6 < pi/2 is -(2pi)/3 <x< pi/3

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-pi/2 <x+pi/6 < pi/2

- \frac{π}{2} < x + \frac{π}{6} < \frac{π}{2}

- \frac{2 π}{3} < x < \frac{π}{3}

Interval Notation

(- \frac{2 π}{3}, \frac{π}{3})

Decimal Notation

- 2.09439 \dots < x < 1.04719 \dots

Solution steps

- \frac{π}{2} < x + \frac{π}{6} < \frac{π}{2}

a < u < b

then

a < u and u < b

- \frac{π}{2} < x + \frac{π}{6} and x + \frac{π}{6} < \frac{π}{2}

- \frac{π}{2} < x + \frac{π}{6} : x > - \frac{2 π}{3}

x + \frac{π}{6} < \frac{π}{2} : x < \frac{π}{3}

Combine the intervals

x > - \frac{2 π}{3} and x < \frac{π}{3}

Merge Overlapping Intervals

- \frac{2 π}{3} < x < \frac{π}{3}

6 x^{2} + 12 x - 18

3. 4^{2}

5 x^{2} = - 3 x + 3

(\frac{4}{x})^{3}

\frac{2 π}{\frac{1}{3}}

What is -pi/2 <x+pi/6 < pi/2 ?
The solution to -pi/2 <x+pi/6 < pi/2 is -(2pi)/3 <x< pi/3