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`(1)/(2) ((3x)/(5) + 4 )ge (1)/(3) (x - 6)`A. `[120, oo]`B. `(-oo, 120]`C. `[0, 120]`D. `[-120, 0]` |
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Answer» Correct Answer - B We have, `(1)/(2) ((3x)/(5) + 4) ge (1)/(3)(x-6)` `rArr (1)/(2) ((3x+20)/(5) ) ge (1)/(3)(x-6)` `rArr (3x + 20)/(10) ge (x-6)/(3)` `rArr 3(3x + 20) ge 10 (x-6) " " ["Multiplying both sides by 30 i.e the LCM of 10 and 3"]` `rArr 9x+60 ge 10x-60` `rArr 9x-10x ge -60-60` `rArr -x ge -120 ` `rArr x le 120` `rArr x in (-oo, 120]` Hence, the solution set of the given inequation is `(-oo, 120]`, REMARK The solution set of simultaneous inequations is the intersection of their solution sets. |
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