Question

Solve the inequality. Suggestion: A calculator may be useful for approximating key numbers.

x2 − 9x + 18 > 0

(3, 6) ∪ (6, )
(−, 3) ∪ (6, )
(3, 6) (6, )
(−, 3)
The missing spaces are infinity signs.. HELP Por favorrrrrr:)

Answer 1

second one

Answer 2

\[(-\infty, 3)\cup (6,\infty)\]

Answer 3

\[x^2 − 9x + 18 =(x-3)(x-6)\] is a parabola that opens up, it will be positive outside the zeros and negative between them. zeros are 3 and 6 which is how you get the answer

Answer 4

All you have to do here is factor the quadratic. If you factor out \[x^{2} - 9x + 18\]
it simplifies to \[(x - 6)(x - 3)\]

You then make a number line with those as your points.


Test a number between infinity and 3. Test a number between 3 and 6. Then test a number between 6 and infinity. If your test case satisfies the inequality, its valid for that part.

After testing, you get \[(-\infty,3)\cup(6,\infty)\]

Hope that helps!