What is -2<(x^2-2)/(1-2x)<= 2 ?

The solution to -2<(x^2-2)/(1-2x)<= 2 is -2(1+sqrt(2))<= x<0\lor 2(sqrt(2)-1)<= x<4

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-2<(x^2-2)/(1-2x)<= 2

- 2 < \frac{x ^{2} - 2}{1 - 2 x} \leq 2

- 2 (1 + 2) \leq x < 0 or 2 (2 - 1) \leq x < 4

Interval Notation

[- 2 (1 + 2), 0) \cup [2 (2 - 1), 4)

Decimal Notation

- 4.82842 \dots \leq x < 0 or 0.82842 \dots \leq x < 4

Solution steps

- 2 < \frac{x ^{2} - 2}{1 - 2 x} \leq 2

a < u \leq b

then

a < u and u \leq b

- 2 < \frac{x ^{2} - 2}{1 - 2 x} and \frac{x ^{2} - 2}{1 - 2 x} \leq 2

- 2 < \frac{x ^{2} - 2}{1 - 2 x} : x < 0 or \frac{1}{2} < x < 4

\frac{x ^{2} - 2}{1 - 2 x} \leq 2 : - 2 (1 + 2) \leq x < \frac{1}{2} or x \geq 2 (2 - 1)

Combine the intervals

(x < 0 or \frac{1}{2} < x < 4) and (- 2 (1 + 2) \leq x < \frac{1}{2} or x \geq 2 (2 - 1))

Merge Overlapping Intervals

- 2 (1 + 2) \leq x < 0 or 2 (2 - 1) \leq x < 4

3 x^{2} - 2 x - 21

(\frac{13}{7})^{2}

3 (\frac{1}{2})

3 b c - 2 b - 10 + 15 c

x^{4} - 40 x^{2} + 144

What is -2<(x^2-2)/(1-2x)<= 2 ?
The solution to -2<(x^2-2)/(1-2x)<= 2 is -2(1+sqrt(2))<= x<0\lor 2(sqrt(2)-1)<= x<4