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 $$x + 2 > \frac { 12 } { | x + 3 | }$$

6. (a) Find, in the simplest surd form where appropriate, the exact values of \(x\) for which $$\frac { x } { 2 } + 3 = \left| \frac { 4 } { x } \right|$$ (b) Sketch, on the same axes, the line with equation \(y = \frac { x } { 2 } + 3\) and the graph of \(y = \left| \frac { 4 } { x } \right| , \quad x \neq 0\).
(c) Find the set of values of \(x\) for which \(\frac { x } { 2 } + 3 > \left| \frac { 4 } { x } \right|\).
(2)(Total 10 marks)