Find the set of values of $x$ for which (a) $4x - 5 > 15 - x$ (b) $x(x - 4) > 12$ - Edexcel - A-Level Maths Pure - Question 5 - 2012 - Paper 1

To solve the inequality $x(x - 4) > 12$, we rearrange it first:

1. Rewrite the inequality as: $x^2 - 4x - 12 > 0$.

2. Now, factor the quadratic: $x^2 - 4x - 12 = (x - 6)(x + 2) > 0$.

3. Identify the critical points, which are $x = 6$ and $x = -2$.

4. Create a number line and test intervals determined by these critical points, which are $(- o -2)$, $(-2, 6)$, and $(6, + o ext{infinity})$:

   • For $x < -2$, choose $x = -3$: $(-3)(-3 - 4) > 12$ (true).
   • For $-2 < x < 6$, choose $x = 0$: $(0)(0 - 4) > 12$ (false).
   • For $x > 6$, choose $x = 7$: $(7)(7 - 4) > 12$ (true).

5. Therefore, the solution set for part (b) is: $x < -2 ext{ or } x > 6$.