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On the number line, which open interval represents \( |x+4|<6 \)?संख्या रेखा पर \( |x+4|<6 \) को कौन-सा खुला अंतराल (open interval) दर्शाता है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \( (-10,2) \)\( (-10,2) \)
\( |x+4|<6 \) means the distance of \(x\) from \(-4\) is less than \(6\). So \(-6<x+4<6\). Subtract \(4\) throughout: \(-10<x<2\). Since it is \(<6\) (strict inequality), the endpoints \(-10\) and \(2\) are not included, so the interval is \( (-10,2) \).\( |x+4|<6 \) का अर्थ है कि \(x\) और \(-4\) के बीच की दूरी \(6\) से कम है। इसलिए \(-6<x+4<6\)। अब पूरे व्यंजक से \(4\) घटाएँ: \(-10<x<2\)। क्योंकि असमिका \(<6\) है (सख्त असमानता), इसलिए सिरों \(-10\) और \(2\) को शामिल नहीं किया जाता; अतः अंतराल \( (-10,2) \) है।
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