Question

The set of values of \( x \) satisfying the system of inequalities \( 5x + 2 < 3x + 8 \) and \( \frac{x^2}{x-1} < 4 \) is:

• A. \( (-\infty, 1) \)
• B. \( (3, \infty) \)
• C. \( (-\infty, 1) \cup (2, 3) \)
• D. \( (-\infty, 1) \cup (2, 3) \cup (5, \infty) \)

Hint:

When solving inequalities, always consider the domain restrictions, especially when dealing with rational functions.

Answer 1

The Correct Option is D

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 \( (-\infty, 1) \cup (2, 3) \cup (5, \infty) \).