What is log_{|x|}(sqrt(9-x^2)-x-1)>= 1 ?

The solution to log_{|x|}(sqrt(9-x^2)-x-1)>= 1 is -2sqrt(2)<= x<-1\lor (2sqrt(11)-2)/5 <= x<1

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log_{|x|}(sqrt(9-x^2)-x-1)>= 1

lo g_{∣ x ∣} (9 - x^{2} - x - 1) \geq 1

- 22 \leq x < - 1 or \frac{2 11 - 2}{5} \leq x < 1

Interval Notation

[- 22, - 1) \cup [\frac{2 11 - 2}{5}, 1)

Decimal Notation

- 2.82842 \dots \leq x < - 1 or 0.92664 \dots \leq x < 1

Solution steps

lo g_{∣ x ∣} (9 - x^{2} - x - 1) \geq 1

Find positive and negative intervals

x < 0, x \geq 0

Solve the inequality for each interval

- 22 \leq x < - 1 or No Solution or \frac{2 11 - 2}{5} \leq x < 1

Merge Overlapping Intervals

- 22 \leq x < - 1 or \frac{2 11 - 2}{5} \leq x < 1

∣ 3 x - 2 ∣ + ∣ x + 4 ∣ > 8

\frac{2}{x - 12} > \frac{6}{5}

2 < ∣ x - 1 ∣ + ∣ x - 3 ∣

lo g_{x^{2}} (\frac{( 4 x - 5 )}{∣ x - 2 ∣}) \geq \frac{1}{2}

∣ 2 x - 2 ∣ \leq 6

What is log_{|x|}(sqrt(9-x^2)-x-1)>= 1 ?
The solution to log_{|x|}(sqrt(9-x^2)-x-1)>= 1 is -2sqrt(2)<= x<-1\lor (2sqrt(11)-2)/5 <= x<1