What is -0.1<= (sqrt((x+3))-sqrt(3)-x)/((2sqrt(3))) ?

The solution to -0.1<= (sqrt((x+3))-sqrt(3)-x)/((2sqrt(3))) is -3<= x<= 0.47977…

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-0.1<= (sqrt((x+3))-sqrt(3)-x)/((2sqrt(3)))

- 0.1 \leq \frac{( x + 3 ) - 3 - x}{( 2 3 )}

- 3 \leq x \leq 0.47977 \dots

Solution steps

- 0.1 \leq \frac{x + 3 - 3 - x}{2 3}

Switch sides

\frac{x + 3 - 3 - x}{2 3} \geq - 0.1

Multiply both sides by

23

\frac{( x + 3 - 3 - x ) \cdot 2 3}{2 3} \geq (- 0.1) \cdot 23

Simplify

x + 3 - 3 - x \geq - 3 \cdot 0.2

Subtract

- 3 - x

from both sides

x + 3 - 3 - x - (- 3 - x) \geq - 3 \cdot 0.2 - (- 3 - x)

Simplify

x + 3 \geq 3 \cdot 0.8 + x

f (x) \geq g (x)

then

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

For

3 \cdot 0.8 + x < 0 : x < - \frac{4 3}{5}

For

3 \cdot 0.8 + x \geq 0 : - \frac{4 3}{5} \leq x \leq 0.47977 \dots

Find singularity points

Find non-negative values for radicals:

x \geq - 3

Combine the intervals

(- \frac{4 3}{5} \leq x \leq 0.47977 \dots or x < - \frac{4 3}{5}) and x \geq - 3

Merge Overlapping Intervals

- 3 \leq x \leq 0.47977 \dots

Verify Solutions:

- 3 \leq x \leq 0.47977 \dots

True

The solution is

- 3 \leq x \leq 0.47977 \dots

13 x - 15 = 12 x + 16

\frac{2 x - 3}{x + 1} \geq 2

6 - 3 q \leq 1

6 - 6 ∣ v + 7 ∣ = - 84

\frac{1}{5} \cdot \frac{1}{5}

What is -0.1<= (sqrt((x+3))-sqrt(3)-x)/((2sqrt(3))) ?
The solution to -0.1<= (sqrt((x+3))-sqrt(3)-x)/((2sqrt(3))) is -3<= x<= 0.47977…