KCET · Maths · Basic of Mathematics
If \( |x+5| \geq 10 \) then
- A \( x \in(-15,5] \)
- B \( x \in(-5,5] \)
- C \( x \in(-\infty,-15] \cup[5, \infty) \)
- D \( x \in[-\infty,-15] \cup[5, \infty) \)
Answer & Solution
Correct Answer
(C) \( x \in(-\infty,-15] \cup[5, \infty) \)
Step-by-step Solution
Detailed explanation
Given that, \(|x+5| \geq 10\)
\(\Rightarrow-10 \geq x+5 \geq 10\)
\(\Rightarrow-15 \geq x \geq 5\)
\(\Rightarrow x \in(-\infty,-15] \cup[5, \infty)\)
\(\Rightarrow-10 \geq x+5 \geq 10\)
\(\Rightarrow-15 \geq x \geq 5\)
\(\Rightarrow x \in(-\infty,-15] \cup[5, \infty)\)
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