Solve x-2x+5>2. - Mathematics

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Sum

Solve `(x - 2)/(x + 5) > 2`.

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Solution

We have,  `(x - 2)/(x + 5) > 2`

⇒ `(x - 2)/(x + 5) - 2 > 0`  .......[Subtracting 2 from each side]

⇒ `(-(x + 12))/(x + 5) > 0`

⇒ `(x + 12)/(x + 5) < 0`   .......(Multiplying both sides by –1)

⇒ x + 12 > 0 and x + 5 < 0   .....[Since `a/b < 0` ⇒ a and b are of opposite signs.]

or

x + 12 < 0 and x + 5 > 0

⇒ x > –12 and x < –5

or 

x < –12 and x > –5   .....(Not possible)

Therefore, –12 < x < –5 i.e. x ∈ (–12, –5).

Concept: Inequalities - Introduction
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APPEARS IN

NCERT Mathematics Exemplar Class 11
Chapter 6 Linear Inequalities
Solved Examples | Q 2 | Page 100
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