What is |x^2-2x-2|>= |x^2-2| ?

The solution to |x^2-2x-2|>= |x^2-2| is x<=-1\lor 0<= x<= 2

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|x^2-2x-2|>= |x^2-2|

x^{2} - 2 x - 2 \geq x^{2} - 2

x \leq - 1 or 0 \leq x \leq 2

Interval Notation

(- \infty, - 1] \cup [0, 2]

Solution steps

x^{2} - 2 x - 2 \geq x^{2} - 2

Find positive and negative intervals

x \leq - 2, - 2 < x \leq - 3 + 1, - 3 + 1 < x < 2, 2 \leq x < 3 + 1, x \geq 3 + 1

Solve the inequality for each interval

x \leq - 2 or - 2 < x \leq - 1 or 0 \leq x < 2 or 2 \leq x \leq 2 or No Solution

Merge Overlapping Intervals

x \leq - 1 or 0 \leq x \leq 2

∣ x - 2 ∣ \leq 2 x^{2} - 9 x + 9

\frac{( x ^{2} - ∣ x ∣ - 12 )}{( x - 3 )} \geq 2 x

∣ t ∣ < 1

\frac{x}{( x ^{2} - x - 1 )} \leq 2

∣ 3 x - 4 ∣ > 2 - 5 x

What is |x^2-2x-2|>= |x^2-2| ?
The solution to |x^2-2x-2|>= |x^2-2| is x<=-1\lor 0<= x<= 2