Question:
The set of values of \( x \) satisfying the system of inequalities \( 5x + 2 < 3x + 8 \) and \( \frac{x^2}{x-1} < 4 \) is:
The set of values of \( x \) satisfying the system of inequalities \( 5x + 2 < 3x + 8 \) and \( \frac{x^2}{x-1} < 4 \) is:
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When solving inequalities, always consider the domain restrictions, especially when dealing with rational functions.
Updated On: Apr 1, 2025
- \( (-\infty, 1) \)
- \( (3, \infty) \)
- \( (-\infty, 1) \cup (2, 3) \)
- \( (-\infty, 1) \cup (2, 3) \cup (5, \infty) \)
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The Correct Option is D
Solution and Explanation
The solution of the inequality system can be found by solving both inequalities and analyzing the solution intervals.
The solution for \( 5x + 2 < 3x + 8 \) gives \( x < 3 \), and solving \( \frac{x^2}{x-1} < 4 \) gives the final solution set as \( (-\infty, 1) \cup (2, 3) \cup (5, \infty) \).
The solution for \( 5x + 2 < 3x + 8 \) gives \( x < 3 \), and solving \( \frac{x^2}{x-1} < 4 \) gives the final solution set as \( (-\infty, 1) \cup (2, 3) \cup (5, \infty) \).
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