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Solve the compound inequality \(7-4x<3(2-x)\le 12\).युग्म असमानता \(7-4x<3(2-x)\le 12\) को हल कीजिए।
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(x>1\)\(x>1\)
From the first part, \(7-4x<3(2-x)\) becomes \(7-4x<6-3x\), which gives \(x>1\). The second part, \(3(2-x)\le12\), becomes \(6-3x\le12\), giving \(x\ge-2\). The intersection of these two conditions is \(x>1\), so option D is correct. Remember to reverse the inequality sign when multiplying or dividing by a negative number.पहले, \(7-4x<3(2-x)\) से \(7-4x<6-3x\), अतः \(x>1\) प्राप्त होता है। दूसरे भाग, \(3(2-x)\le12\), से \(6-3x\le12\), इसलिए \(x\ge-2\) मिलता है। दोनों शर्तों का प्रतिच्छेद \(x>1\) है, इसलिए विकल्प D सही है। ध्यान रखें कि ऋणात्मक संख्या से भाग देने या गुणा करने पर असमानता का चिह्न उलट जाता है।
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