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

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

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

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

- \frac{π}{3} < x < \frac{2 π}{3}

Interval Notation

(- \frac{π}{3}, \frac{2 π}{3})

Decimal Notation

- 1.04719 \dots < x < 2.09439 \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{π}{3}

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

Combine the intervals

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

Merge Overlapping Intervals

- \frac{π}{3} < x < \frac{2 π}{3}

- 5 x (2 x - 9) = 2 (x - 8) - 11

6 x^{2} - 12 x - 38 = 10

3 x^{2} - 7 x + 3 = 0

p^{2} + 11 p - 12 = 0

- 5 \leq \frac{x - 2}{- 5} < 2

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