Answer
$x \lt 1~~$ or $~~x \gt 2$
The solution set is $~~(-\infty, 1)\cup (2,\infty)$
Work Step by Step
$(x-1)(x-2) \gt 0$
When $~~x=1~~$ or $~~x=2,~~$ then $~~(x-1)(x-2) = 0$
When $x \lt 1,~~$ then $~~(x-1)(x-2) \gt 0$
When $1 \lt x \lt 2,~~$ then $~~(x-1)(x-2) \lt 0$
When $x \gt 2,~~$ then $~~(x-1)(x-2) \gt 0$
Solution:
$x \lt 1~~$ or $~~x \gt 2$
The solution set is $~~(-\infty, 1)\cup (2,\infty)$
