Search any question & find its solution
Question:
Answered & Verified by Expert
The set \( A=\{x ;|2 x+3| < 7\} \) is equal to the set.
Options:
Solution:
1872 Upvotes
Verified Answer
The correct answer is:
\( D=\{x: 0 < x+5 < 7\} \)
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
$D=\{x: 0 < x+5 < 7\}$
$\Rightarrow|2 x+3| < 7 \rightarrow < 2 x+3 < 7$
$\Rightarrow 10 < 2 x < 4 \Rightarrow-5 < x < 2$
$\Rightarrow 0 < x+5 < 7$
Therefore, $\operatorname{set} A=\{x:|2 x+3| < 7\}$ is equal to
$D=\{x: 0 < x+5 < 7\}$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.