Q99 / 180 · KCET 2014 · Mathematics

The set $ A=\{x ;|2 x+3| < 7\} $ is equal to the set.

A
$ B=\{x:-3 < x < 7\} $
B
$ C=\{x:-13 < 2 x < 4\} $
Correct answer
C
$ D=\{x: 0 < x+5 < 7\} $
D
$ E=\{x:-7 < x < 7\} $

Solution

Given $\mathrm{A}=\{x ;|2 x+3| < 7\}$ $\Rightarrow|2 x+3| < 7 \rightarrow < 2 x+3 < 7$ $\Rightarrow 10 < 2 x < 4 \Rightarrow-5 < x < 2$ $\Rightarrow 0 < x+5 < 7$ Therefore, $\operatorname{set} A=\{x:|2 x+3| < 7\}$ is equal to $D=\{x: 0 < x+5 < 7\}$

Hence, the correct answer is option: 'C'.

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The set \( A=\{x ;|2 x+3| < 7\} \) is equal to the set.

Solution

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