What is x-sqrt(1-|x|)<= 0 ?

The solution to x-sqrt(1-|x|)<= 0 is -1<= x<= (sqrt(5)-1)/2

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x-sqrt(1-|x|)<= 0

x - 1 - ∣ x ∣ \leq 0

- 1 \leq x \leq \frac{5 - 1}{2}

Interval Notation

[- 1, \frac{5 - 1}{2}]

Decimal Notation

- 1 \leq x \leq 0.61803 \dots

Solution steps

x - 1 - ∣ x ∣ \leq 0

Subtract

x

from both sides

x - 1 - ∣ x ∣ - x \leq 0 - x

Simplify

- 1 - ∣ x ∣ \leq - x

Multiply both sides by

- 1

(reverse the inequality)

(- 1 - ∣ x ∣) (- 1) \geq (- x) (- 1)

Simplify

1 - ∣ x ∣ \geq x

f (x) \geq g (x)

then

g (x) < 0 or g (x) \geq 0

For

x < 0 : x < 0

For

x \geq 0 : 0 \leq x \leq \frac{5 - 1}{2}

Find singularity points

Find non-negative values for radicals:

- 1 \leq x \leq 1

Combine the intervals

(0 \leq x \leq \frac{5 - 1}{2} or x < 0) and - 1 \leq x \leq 1

Merge Overlapping Intervals

- 1 \leq x \leq \frac{5 - 1}{2}

Verify Solutions:

- 1 \leq x \leq \frac{5 - 1}{2}

True

The solution is

- 1 \leq x \leq \frac{5 - 1}{2}

3 - x \leq 1 - x

x + 3 + x + 2 - 2 x + 4 > 0

lo g_{x} (x) < 2

x - 1 > 3 - x

x^{2} - 4 x > x - 2

What is x-sqrt(1-|x|)<= 0 ?
The solution to x-sqrt(1-|x|)<= 0 is -1<= x<= (sqrt(5)-1)/2