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


Question

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

Options

A) -3 < x < 1

B) x 1

C) -3 < x < 5

D) 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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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

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