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What is the solution of the following inequality? \(8-2(3x+1)\leq 0\)निम्नलिखित असमता का हल क्या है? \(8-2(3x+1)\leq 0\)
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(x\geq 1\)\(x\geq 1\)
Expanding the brackets gives \(8-6x-2\leq 0\), or \(6-6x\leq 0\). Thus, \(-6x\leq -6\). Dividing both sides by \(-6\) reverses the inequality sign, so \(x\geq 1\). Exam tip: whenever an inequality is multiplied or divided by a negative number, reverse the inequality sign.कोष्ठक खोलने पर \(8-6x-2\leq 0\), अर्थात् \(6-6x\leq 0\) मिलता है। अतः \(-6x\leq -6\)। दोनों पक्षों को \(-6\) से विभाजित करने पर असमता का चिह्न उलट जाता है, इसलिए \(x\geq 1\)। परीक्षा-युक्ति: किसी असमता को ऋणात्मक संख्या से गुणा या भाग करने पर \(\leq\) और \(\geq\) आपस में बदल जाते हैं।
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