What is sqrt(x^2+3x)<1-x ?

The solution to sqrt(x^2+3x)<1-x is x<=-3\lor 0<= x< 1/5

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sqrt(x^2+3x)<1-x

x^{2} + 3 x < 1 - x

x \leq - 3 or 0 \leq x < \frac{1}{5}

Interval Notation

(- \infty, - 3] \cup [0, \frac{1}{5})

Decimal Notation

x \leq - 3 or 0 \leq x < 0.2

Solution steps

x^{2} + 3 x < 1 - x

f (x) < g (x)

then

g (x) > 0

1 - x > 0 : x < 1

x^{2} + 3 x < 1 - x : x < \frac{1}{5}

Find singularity points

Find non-negative values for radicals:

x \leq - 3 or x \geq 0

Combine the intervals

x < 1 and x < \frac{1}{5} and (x \leq - 3 or x \geq 0)

Merge Overlapping Intervals

x \leq - 3 or 0 \leq x < \frac{1}{5}

Verify Solutions:

x \leq - 3

True

, 0 \leq x < \frac{1}{5}

True

The solution is

x \leq - 3 or 0 \leq x < \frac{1}{5}

- (\frac{4}{3})^{3}

5 x^{2} y - 20 y

\frac{2}{5}

12 \cdot x = 48

\frac{5}{12} - \frac{5}{12} x + x = \frac{1}{2}

What is sqrt(x^2+3x)<1-x ?
The solution to sqrt(x^2+3x)<1-x is x<=-3\lor 0<= x< 1/5