Sum

Solve the inequation:

`("x" + 5)/("x" - 3) < 0`

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#### Solution

`("x" + 5)/("x" - 3) < 0`

We know that if `"a"/"b" < 0` when a > 0 and b < 0 or a < 0 and b > 0

∴ either x + 5 > 0 and x – 3 < 0

or x + 5 < 0 and x – 3 > 0**Case I:**

x + 5 > 0 and x – 3 < 0

∴ x > – 5 and x < 3

∴ − 5 < x < 3

∴ solution set = (−5, 3)**Case II:**

x + 5 < 0 and x – 3 > 0

∴ x < – 5 and x > 3

which is not possible

∴ solution set = ø

∴ solution set of the given inequation is (– 5, 3)

Concept: Solution of Linear Inequality

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