Question 3 - A-Level Maths

Find the set of values of $x$ for which
1. $6 x - 11 > x + 4$,
2. $x ^ { 2 } - 6 x - 16 < 0$.
3. (i) Sketch on the same diagram the graphs of $y = ( x - 1 ) ^ { 2 } ( x - 5 )$ and $y = 8 - 2 x$.
Label on your diagram the coordinates of any points where each graph meets the coordinate axes.
Explain how your diagram shows that there is only one solution, $\alpha$, to the equation $$( x - 1 ) ^ { 2 } ( x - 5 ) = 8 - 2 x$$
State the integer, $n$, such that $$n < \alpha < n + 1 .$$