What is the solution of \(\frac{x – 5}{x + 3} < -1\)?
-
-3 < x < 1
- x < -3 or x > 1
- -3 < x < 5
- x < -3 or x > 5
The correct answer is: A
Explanation
Consider the range -3 < x < -1= { -2, -1, 0}, for instance
When x = -2,
\(\frac{-2 - 5}{-2 + 3} < -1\)
\(\frac{-7}{1} < -1\)
When x = -1,
\(\frac{-1 - 5}{-1 + 3} < -1\)
\(\frac{-6}{2} < -1\)
= -3 < -1
When x = 0,
\(\frac{0 - 5}{0 + 3} < -1\)
\(\frac{- 5}{3} < -1\)
Hence -3 < x < 1
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