If |x + 5 | < 3, then : (a) −8 < x < 8 (b) −2 < x < 2 (c) 2 < x

1.	If \|x + 5 \| < 3, then : (a) −8 < x < 8 (b) −2 < x < 2 (c) 2 < x < 8 (d) −8 < x < − 2
Answer» Correct option (d) −8 < x < − 2 Explanation: \|x + 5 \| < 3 ⇒ x + 5 < 3 and −x − 5 < 3 ⇒ x < 3 − 5 and −5 − 3 < x ⇒ x < − 2 and − 8 < x ⇒ − 8 < x < − 2.

If |x + 5 | < 3, then : (a) −8 < x < 8 (b) −2 < x < 2 (c) 2 < x < 8 (d) −8 < x < − 2

Answer»

Correct option (d) −8 < x < − 2

Explanation:

|x + 5 | < 3

⇒ x + 5 < 3 and −x − 5 < 3

⇒ x < 3 − 5 and −5 − 3 < x

⇒ x < − 2 and − 8 < x

⇒ − 8 < x < − 2.

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If |x + 5 | &lt; 3, then : (a) −8 &lt; x &lt; 8 (b) −2 &lt; x &lt; 2 (c) 2 &lt; x &lt; 8 (d) −8 &lt; x &lt; − 2

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If |x + 5 | < 3, then : (a) −8 < x < 8 (b) −2 < x < 2 (c) 2 < x < 8 (d) −8 < x < − 2