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Question
Solve
\[\left| x + \frac{1}{3} \right| > \frac{8}{3}\]
Solution
\[\text{ As }, \left| x + \frac{1}{3} \right| > \frac{8}{3}\]
\[ \Rightarrow \left( x + \frac{1}{3} \right) < \frac{- 8}{3} \text{ or } \left( x + \frac{1}{3} \right) > \frac{8}{3} \left( \text{ As }, \left| x \right| > a \Rightarrow x < - a or x > a \right)\]
\[ \Rightarrow x < - \frac{1}{3} - \frac{8}{3} \text{ or } x > \frac{8}{3} - \frac{1}{3}\]
\[ \Rightarrow x < - \frac{9}{3} \text{ or } x > \frac{7}{3}\]
\[ \Rightarrow x < - 3 \text{ or } x > \frac{7}{3}\]
\[ \therefore x \in \left( - \infty , - 3 \right) \cup \left( \frac{7}{3}, \infty \right)\]
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