Write the set of values of *x* satisfying the inequations 5*x* + 2 < 3*x* + 8 and \[\frac{x + 2}{x - 1} < 4\]

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#### Solution

\[\text{ We have }, \]

\[5x + 2 < 3x + 8 \text{ and } \frac{x + 2}{x - 1} < 4\]

\[ \Rightarrow 2x < 6 \text{ and } \frac{x + 2}{x - 1} - 4 < 0\]

\[ \Rightarrow x < 3 \text{ and } \frac{x + 2 - 4x + 4}{x - 1} < 0\]

\[ \Rightarrow x \in ( - \infty , 3) \text{ and } \frac{- 3x + 6}{x - 1} < 0\]

\[ \Rightarrow x \in ( - \infty , 3) \text{ and } \frac{- x + 2}{x - 1} < 0\]

\[\text{ For } \frac{- x + 2}{x - 1} < 0, \text{ critical points are 1 and } 2 . \]

\[ \Rightarrow x \in (2, \infty ) \cup ( - \infty , 1)\]

\[ \therefore x \in ( - \infty , 1) \cup (2, 3)\]

Is there an error in this question or solution?

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