Solving $x^2 - 16 x+55> 0$ for $x$ Solving $x^2 - 16 x+55&gt; 0$ for $x$

my work 

$$(x-11)(x-5) &gt; 0$$

then  x >11 and x > 5

is that correct ???
Draw out the parabola $y=x^2-16x+55$ , using a graphics calculator 

We can clearly see that when $x&gt;11$ and $x&lt;5$ the inequality is satisfied.
Yes, the first part of your argument is right

But Carefully introspect the case that 2 negative numbers when multiplied also gives a positive number number

I recommend using the wavy curve method to check your solution to  the above inequality

$\quad x\quad \in \quad (-\infty ,5)\cup (11,\infty )$