Solve inequality with reciprocal in modulus

1. (a) Use algebra to determine the set of values of \(x\) for which

$$x - 5 < \frac { 9 } { x + 3 }$$ (b) Hence, or otherwise, determine the set of values of \(x\) for which $$x - 5 < \frac { 9 } { | x + 3 | }$$

3. (a) Find the set of values of \(x\) for which $$x + 4 > \frac { 2 } { x + 3 }$$ (b) Deduce, or otherwise find, the values of \(x\) for which $$x + 4 > \frac { 2 } { | x + 3 | }$$

1. (a) Use algebra to find the set of values of \(x\) for which

$$x + 2 > \frac { 12 } { x + 3 }$$ (b) Hence, or otherwise, find the set of values of \(x\) for which $$x + 2 > \frac { 12 } { | x + 3 | }$$

1. In this question you must show all stages of your working.

Solutions relying entirely on calculator technology are not acceptable. \begin{figure}[h] \end{figure} Figure 1 shows a sketch of the curve with equation \(y = \frac { x ^ { 2 } - 2 x - 24 } { | x + 6 | }\) and the line with equation \(y = 5 - 4 x\) Use algebra to determine the values of \(x\) for which $$\frac { x ^ { 2 } - 2 x - 24 } { | x + 6 | } < 5 - 4 x$$