What is the solution of \(\frac{x - 5}{x + 3} < -1\)?
A
-3 < x < 1
B
x 1
C
-3 < x < 5
D
x 5
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
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
Source: Myschool Past Questions Archive (Record #27010)