Answer:
x ∈ (-∞, 3) U (6, ∞).
Step-by-step explanation:
[tex]x^2> 9x - 18[/tex]
[tex]x^2 - 9x + 18> 0[/tex]
We use factorization and optain
[tex](x-6)(x-3)> 0[/tex]
Then, we have two critical points: x=3 and x=6. Now:
(i) for x < 3 we have that x-6 <0 and x-3 <0. Then (x-6)(x-3) > 0.
(ii) for 3 < x < 6 we have that x -6 <0 and x -3 > 0. Then (x-6)(x-3) < 0.
(iii) for x > 6 we have that x-6 >0 and x-3 > 0. Then, (x-6)(x-3) > 0.
conditions (i) and (iii) satisfy the inequatliy, then the solution is x ∈ (-∞, 3) U (6, ∞).
The graph is in the picture below.
