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BITSAT 2013

Exam: BITSAT
Year: 2013
Subject: Mathematics
Chapter: Basics of Mathematics

BITSAT 2013 · Mathematics · Basics of Mathematics

The set of all real x satisfying the inequality (3-|x|)/(4-|x|) ≥...

The set of all real

x

satisfying the inequality

\frac{3-|x|}{4-|x|} \geq 0,

is

Options

A[-3,3] $\cup(-\infty,-4) \cup(4, \infty)$
B $(-\infty,-4) \cup(4, \infty)$
C $(-\infty,-3) \cup(4, \infty)$
D $(-\infty,-3) \cup(3, \infty)$

Correct answer

A. [-3,3] $\cup(-\infty,-4) \cup(4, \infty)$

Step-by-step solution

Given,

\frac{3-|x|}{4-|x|} \geq 0\Rightarrow 3-|x| \leq 0

and

4-|x|< 0

or

3-|x| \geq 0

and

4-|x|< 0\Rightarrow|x| \geq 3

and

|x| > 4

or

|x| \leq 3

and

|x|< 4\Rightarrow|x| > 4

or

|x| \leq 3\Rightarrow x \in(-\infty,-4) \cup[-3,3] \cup(4, \infty)

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