What is sqrt(-3x)-sqrt(x+4)>= 0 ?

The solution to sqrt(-3x)-sqrt(x+4)>= 0 is -4<= x<=-1

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sqrt(-3x)-sqrt(x+4)>= 0

- 3 x - x + 4 \geq 0

- 4 \leq x \leq - 1

Interval Notation

[- 4, - 1]

Solution steps

- 3 x - x + 4 \geq 0

Add

x + 4

to both sides

- 3 x - x + 4 + x + 4 \geq 0 + x + 4

Simplify

- 3 x \geq x + 4

f (x) \geq g (x)

then

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

For

x + 4 < 0 :

No Solution

For

x + 4 \geq 0 : x \leq - 1

Find singularity points

Find non-negative values for radicals:

- 4 \leq x \leq 0

Combine the intervals

(x \leq - 1 or No Solution) and - 4 \leq x \leq 0

Merge Overlapping Intervals

- 4 \leq x \leq - 1

- 2 x^{2} + 20 = 3 x - 15

\frac{a ^{2} - ab}{a ^{2} + ab}

0 = - 4.9 t^{2} 2 + 5 t + 185

15 \cdot 35

7 x^{2} + 6 x = - 2

What is sqrt(-3x)-sqrt(x+4)>= 0 ?
The solution to sqrt(-3x)-sqrt(x+4)>= 0 is -4<= x<=-1