What is sqrt(x+2)<= 1/(x+2) ?

The solution to sqrt(x+2)<= 1/(x+2) is -2<x<=-1

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sqrt(x+2)<= 1/(x+2)

x + 2 \leq \frac{1}{x + 2}

- 2 < x \leq - 1

Interval Notation

(- 2, - 1]

Solution steps

x + 2 \leq \frac{1}{x + 2}

f (x) \leq g (x)

then

g (x) \geq 0

\frac{1}{x + 2} \geq 0 : x > - 2

x + 2 \leq \frac{1}{x + 2} : x < - 2 or - 2 < x \leq - 1

Find singularity points

Find non-negative values for radicals:

x \geq - 2

Combine the intervals

x > - 2 and (x < - 2 or - 2 < x \leq - 1) and x \geq - 2

Merge Overlapping Intervals

- 2 < x \leq - 1

Verify Solutions:

- 2 < x \leq - 1

True

The solution is

- 2 < x \leq - 1

- 7200 (1 + x)^{2} + 5300 (1 + x) + 8000 = 0

27 a^{3} - b^{6}

4 (y + 1) - y = 3 (y - 1) + 3

x^{2} - 2 x = - 4

- 2 x^{2} + x + 4 = 0