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Question
Solve each of the following system of equations in R.
5x − 1 < 24, 5x + 1 > −24
Solution
\[5x - 1 < 24\]
\[ \Rightarrow 5x < 24 + 1\]
\[ \Rightarrow x < 5 \]
\[ \Rightarrow x \in \left( - \infty , 5 \right) . . . (i)\]
\[\text{ Also }, 5x + 1 > - 24\]
\[ \Rightarrow 5x > - 24 - 1\]
\[ \Rightarrow x > - 5\]
\[ \Rightarrow x \in ( - 5, \infty ) . . . (ii)\]
\[\text{ Hence, the solution of the given set of inequalities is the intersection of } (i) \text{ and } (ii) . \]
\[\left( - \infty , 5 \right) \cap \left( - 5, \infty \right) = \left( - 5, 5 \right)\]
\[\text{ Thus, the solution of the given set of inequalities is } \left( - 5, 5 \right) .\]
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