N1982 P2 Q4

Given that \({2\mathbf{x} + (\mathbf{x} \cdot \mathbf{b})\mathbf{a} = \mathbf{c}}\), where \({\mathbf{a} \cdot \mathbf{b} \neq -2}\), show that \({\mathbf{x} \cdot \mathbf{b} = \frac{\mathbf{c} \cdot \mathbf{b}}{2 + \mathbf{a} \cdot \mathbf{b}}}\).

Deduce an expression for \({\mathbf{x}}\) in terms of \({\mathbf{a}}\), \({\mathbf{b}}\) and \({\mathbf{c}}\).