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Penyelesaian dari pertidaksamaan 2 a ​ − 6 ( 1 − a ) ​ > 3 a ​ adalah ...

Penyelesaian dari pertidaksamaan  adalah ... 

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penyelesaian dari pertidaksamaan tersebut adalah a > 2 1 ​ .

penyelesaian dari pertidaksamaan tersebut adalah 

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Perhatikan perhitungan berikut! &\frac a3\\\left[\frac a2-\frac{\left(1-a\right)}6\right]\cdot{\color[rgb]{0.0, 0.0, 1.0}6}&>&\left[\frac a3\right]\cdot{\color[rgb]{0.0, 0.0, 1.0}6}\\3a-\left(1-a\right)&>&2a\\3a-1+a&>&2a\\4a-1&>&2a\\4a-1+{\color[rgb]{0.0, 0.0, 1.0}1}&>&2a+{\color[rgb]{0.0, 0.0, 1.0}1}\\4a&>&2a+1\\4a-{\color[rgb]{0.0, 0.0, 1.0}2}{\color[rgb]{0.0, 0.0, 1.0}a}&>&2a+1-{\color[rgb]{0.0, 0.0, 1.0}2}{\color[rgb]{0.0, 0.0, 1.0}a}\\2a&>&1\\\frac{2a}{\color[rgb]{0.0, 0.0, 1.0}2}&>&\frac1{\color[rgb]{0.0, 0.0, 1.0}2}\\a&>&\frac12\end{array}" data-mathml="«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mtable columnspacing=¨0px¨ columnalign=¨right center left¨»«mtr»«mtd»«mfrac»«mi»a«/mi»«mn»2«/mn»«/mfrac»«mo»-«/mo»«mfrac»«mfenced»«mrow»«mn»1«/mn»«mo»-«/mo»«mi»a«/mi»«/mrow»«/mfenced»«mn»6«/mn»«/mfrac»«/mtd»«mtd»«mo»§#62;«/mo»«/mtd»«mtd»«mfrac»«mi»a«/mi»«mn»3«/mn»«/mfrac»«/mtd»«/mtr»«mtr»«mtd»«mfenced open=¨[¨ close=¨]¨»«mrow»«mfrac»«mi»a«/mi»«mn»2«/mn»«/mfrac»«mo»-«/mo»«mfrac»«mfenced»«mrow»«mn»1«/mn»«mo»-«/mo»«mi»a«/mi»«/mrow»«/mfenced»«mn»6«/mn»«/mfrac»«/mrow»«/mfenced»«mo»§#183;«/mo»«mn mathcolor=¨#0000FF¨»6«/mn»«/mtd»«mtd»«mo»§#62;«/mo»«/mtd»«mtd»«mfenced open=¨[¨ close=¨]¨»«mfrac»«mi»a«/mi»«mn»3«/mn»«/mfrac»«/mfenced»«mo»§#183;«/mo»«mn mathcolor=¨#0000FF¨»6«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»3«/mn»«mi»a«/mi»«mo»-«/mo»«mfenced»«mrow»«mn»1«/mn»«mo»-«/mo»«mi»a«/mi»«/mrow»«/mfenced»«/mtd»«mtd»«mo»§#62;«/mo»«/mtd»«mtd»«mn»2«/mn»«mi»a«/mi»«/mtd»«/mtr»«mtr»«mtd»«mn»3«/mn»«mi»a«/mi»«mo»-«/mo»«mn»1«/mn»«mo»+«/mo»«mi»a«/mi»«/mtd»«mtd»«mo»§#62;«/mo»«/mtd»«mtd»«mn»2«/mn»«mi»a«/mi»«/mtd»«/mtr»«mtr»«mtd»«mn»4«/mn»«mi»a«/mi»«mo»-«/mo»«mn»1«/mn»«/mtd»«mtd»«mo»§#62;«/mo»«/mtd»«mtd»«mn»2«/mn»«mi»a«/mi»«/mtd»«/mtr»«mtr»«mtd»«mn»4«/mn»«mi»a«/mi»«mo»-«/mo»«mn»1«/mn»«mo»+«/mo»«mn mathcolor=¨#0000FF¨»1«/mn»«/mtd»«mtd»«mo»§#62;«/mo»«/mtd»«mtd»«mn»2«/mn»«mi»a«/mi»«mo»+«/mo»«mn mathcolor=¨#0000FF¨»1«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»4«/mn»«mi»a«/mi»«/mtd»«mtd»«mo»§#62;«/mo»«/mtd»«mtd»«mn»2«/mn»«mi»a«/mi»«mo»+«/mo»«mn»1«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»4«/mn»«mi»a«/mi»«mo»-«/mo»«mn mathcolor=¨#0000FF¨»2«/mn»«mi mathcolor=¨#0000FF¨»a«/mi»«/mtd»«mtd»«mo»§#62;«/mo»«/mtd»«mtd»«mn»2«/mn»«mi»a«/mi»«mo»+«/mo»«mn»1«/mn»«mo»-«/mo»«mn mathcolor=¨#0000FF¨»2«/mn»«mi mathcolor=¨#0000FF¨»a«/mi»«/mtd»«/mtr»«mtr»«mtd»«mn»2«/mn»«mi»a«/mi»«/mtd»«mtd»«mo»§#62;«/mo»«/mtd»«mtd»«mn»1«/mn»«/mtd»«/mtr»«mtr»«mtd»«mfrac»«mrow»«mn»2«/mn»«mi»a«/mi»«/mrow»«mn mathcolor=¨#0000FF¨»2«/mn»«/mfrac»«/mtd»«mtd»«mo»§#62;«/mo»«/mtd»«mtd»«mfrac»«mn»1«/mn»«mn mathcolor=¨#0000FF¨»2«/mn»«/mfrac»«/mtd»«/mtr»«mtr»«mtd»«mi»a«/mi»«/mtd»«mtd»«mo»§#62;«/mo»«/mtd»«mtd»«mfrac»«mn»1«/mn»«mn»2«/mn»«/mfrac»«/mtd»«/mtr»«/mtable»«/math»" role="math" src="data:image/png;base64,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" style="max-width: none;"> Dengan demikian, penyelesaian dari pertidaksamaan tersebut adalah a > 2 1 ​ .

Perhatikan perhitungan berikut! 

table attributes columnalign right center left columnspacing 0px end attributes row cell a over 2 minus fraction numerator open parentheses 1 minus a close parentheses over denominator 6 end fraction end cell greater than cell a over 3 end cell row cell open square brackets a over 2 minus fraction numerator open parentheses 1 minus a close parentheses over denominator 6 end fraction close square brackets times 6 end cell greater than cell open square brackets a over 3 close square brackets times 6 end cell row cell 3 a minus open parentheses 1 minus a close parentheses end cell greater than cell 2 a end cell row cell 3 a minus 1 plus a end cell greater than cell 2 a end cell row cell 4 a minus 1 end cell greater than cell 2 a end cell row cell 4 a minus 1 plus 1 end cell greater than cell 2 a plus 1 end cell row cell 4 a end cell greater than cell 2 a plus 1 end cell row cell 4 a minus 2 a end cell greater than cell 2 a plus 1 minus 2 a end cell row cell 2 a end cell greater than 1 row cell fraction numerator 2 a over denominator 2 end fraction end cell greater than cell 1 half end cell row a greater than cell 1 half end cell end table 

Dengan demikian, penyelesaian dari pertidaksamaan tersebut adalah 

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3 2 x − 3 ​ ≥ 12

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