What is -pi/2 <x-pi/4 <-pi/2 ?

The solution to -pi/2 <x-pi/4 <-pi/2 is No Solution

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-pi/2 <x-pi/4 <-pi/2

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

No Solution

Solution steps

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

a < u < b

then

a < u and u < b

- \frac{π}{2} < x - \frac{π}{4} and x - \frac{π}{4} < - \frac{π}{2}

- \frac{π}{2} < x - \frac{π}{4} : x > - \frac{π}{4}

x - \frac{π}{4} < - \frac{π}{2} : x < - \frac{π}{4}

Combine the intervals

x > - \frac{π}{4} and x < - \frac{π}{4}

Merge Overlapping Intervals

No Solution

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What is -pi/2 <x-pi/4 <-pi/2 ?
The solution to -pi/2 <x-pi/4 <-pi/2 is No Solution