What is ((|x+2|-|x|))/((sqrt(8-x^2)))>= 0 ?

The solution to ((|x+2|-|x|))/((sqrt(8-x^2)))>= 0 is -1<= x<2sqrt(2)

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((|x+2|-|x|))/((sqrt(8-x^2)))>= 0

\frac{( ∣ x + 2 ∣ - ∣ x ∣ )}{( 8 - x ^{2} )} \geq 0

- 1 \leq x < 22

Interval Notation

[- 1, 22)

Decimal Notation

- 1 \leq x < 2.82842 \dots

Solution steps

\frac{∣ x + 2 ∣ - ∣ x ∣}{8 - x ^{2}} \geq 0

Identify the intervals

- 1 \leq x < 22

\frac{( x - 3 )}{( x + 1 )} \geq \frac{( x + 2 )}{( x - 4 )}

x - 3 < (15 - x)

x - 2 < x - 4

x^{2} - 3 x + 2 > 2 x - 5

x - 4 < 2

What is ((|x+2|-|x|))/((sqrt(8-x^2)))>= 0 ?
The solution to ((|x+2|-|x|))/((sqrt(8-x^2)))>= 0 is -1<= x<2sqrt(2)