What is |x^2+x|-5<0 ?

The solution to |x^2+x|-5<0 is (-sqrt(21)-1)/2 <x<(sqrt(21)-1)/2

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|x^2+x|-5<0

x^{2} + x - 5 < 0

\frac{- 21 - 1}{2} < x < \frac{21 - 1}{2}

Solution steps

x^{2} + x - 5 < 0

Move

5

to the right side

x^{2} + x < 5

Apply absolute rule: If

∣ u ∣ < a, a > 0

then

- a < u < a

- 5 < x^{2} + x < 5

x^{2} + x > - 5 and x^{2} + x < 5

True for all x and \frac{- 21 - 1}{2} < x < \frac{21 - 1}{2}

Merge Overlapping Intervals

\frac{- 21 - 1}{2} < x < \frac{21 - 1}{2}

∣ x - 2 ∣ > ∣ 2 x - 3 ∣

x^{2} - 7 x + 12 < ∣ x - 4 ∣

x^{2} + 3 x > 2 - x^{2}

\frac{( x ^{2} - 3 x - 1 )}{( x ^{2} + x + 1 )} < 3

∣ x ∣ < \frac{2}{x}

What is |x^2+x|-5<0 ?
The solution to |x^2+x|-5<0 is (-sqrt(21)-1)/2 <x<(sqrt(21)-1)/2