What is |x+1|^2+2|x+2|>= 2 ?

The solution to |x+1|^2+2|x+2|>= 2 is x =-1

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|x+1|^2+2|x+2|>= 2

∣ x + 1 ∣^{2} + 2 ∣ x + 2 ∣ \geq 2

x \leq - 5 or x \geq - 1

Interval Notation

(- \infty, - 5] \cup [- 1, \infty)

Decimal Notation

x \leq - 2.23606 \dots or x \geq - 1

Solution steps

∣ x + 1 ∣^{2} + 2 ∣ x + 2 ∣ \geq 2

Find positive and negative intervals

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

Solve the inequality for each interval

x \leq - 5 or No Solution or x \geq - 1

Merge Overlapping Intervals

x \leq - 5 or x \geq - 1

x^{2} - 2 x + ∣ x - 4 ∣ < x^{2} - 3 x + 4

∣ - 6 (n + 5) ∣ > - 12

x^{2} - x - 6 < 6

∣ x - 1 ∣ + ∣ x - 2 ∣ < 7

\frac{( x - 2 )}{( 3 )} < 2

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