# Solve the inequation: x+5x-3<0 - Mathematics and Statistics

Sum

Solve the inequation:
("x" + 5)/("x" - 3) < 0

#### 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)

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#### APPEARS IN

Balbharati Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board
Chapter 8 Linear Inequations
Exercise 8.1 | Q 4. (x) | Page 116