Explanation:
x² - x - 12 < 0
as first indication we try to find the delimiter between valid and invalid values.
that mad we try to find the equality solution :
x² - x - 12 = 0
a = 1
b = -1
c = -12
the solution is
x = (-b ± sqrt(b² - 4ac))/(2a) =
= (1 ± sqrt(1 - 4×1×-12))/2 = (1 ± sqrt(1 + 48))/2 =
= (1 ± sqrt(49))/2 = (1 ± 7)/2
x1 = (1 + 7)/2 = 8/2 = 4
x2 = (1 - 7)/2 = -6/2 = -3
these 2 zero solutions are the limits of our solution interval of valid x values.
we see that when gong beyond them like x = 5 or x - -4, we have no longer a valid value.
and since the inequality is "<", or interval limits must be open (they cannot be included). therefore,
- 3 < x < 4