KCET · Maths · Probability
The set \( A=\{x ;|2 x+3| < 7\} \) is equal to the set.
- A \( B=\{x:-3 < x < 7\} \)
- B \( C=\{x:-13 < 2 x < 4\} \)
- C \( D=\{x: 0 < x+5 < 7\} \)
- D \( E=\{x:-7 < x < 7\} \)
Answer & Solution
Correct Answer
(C) \( D=\{x: 0 < x+5 < 7\} \)
Step-by-step Solution
Detailed explanation
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
\(D=\{x: 0 < x+5 < 7\}\)
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