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What is the solution of $$\frac{x - 5}{x + 3} < -1$$?

Question

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

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

Dicussion (1)

• 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