What is |x^2-2x-5|>= |x^2+4x+1| ?

The solution to |x^2-2x-5|>= |x^2+4x+1| is x<=-2\lor-1<= x<= 1

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|x^2-2x-5|>= |x^2+4x+1|

x^{2} - 2 x - 5 \geq x^{2} + 4 x + 1

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

Interval Notation

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

Solution steps

x^{2} - 2 x - 5 \geq x^{2} + 4 x + 1

Find positive and negative intervals

x \leq - 3 - 2, - 3 - 2 < x \leq - 6 + 1, - 6 + 1 < x < 3 - 2, 3 - 2 \leq x < 6 + 1, x \geq 6 + 1

Solve the inequality for each interval

x \leq - 3 - 2 or - 3 - 2 < x \leq - 2 or - 1 \leq x < 3 - 2 or 3 - 2 \leq x \leq 1 or No Solution

Merge Overlapping Intervals

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

- 2 \leq \frac{c}{2}

\frac{x + 11}{8} = - 3

3 x^{2} + 5 x \leq 2

ln \frac{k + 2}{2 + k} = 0

- - 108

What is |x^2-2x-5|>= |x^2+4x+1| ?
The solution to |x^2-2x-5|>= |x^2+4x+1| is x<=-2\lor-1<= x<= 1