Pertanyaan

Himpunan penyelesaian dari pertidaksamaan ( 3 1 ) 2 x + 1 > 3 x − 1 27 adalah ...

Himpunan penyelesaian dari pertidaksamaan $(\frac{1}{3})^{2 x + 1} > \frac{27}{3 ^{x - 1}}$ adalah ...

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Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah E.

Pembahasan

Pertidaksamaan tersebut dapat diselessaikan dengan melakukan manipulasi aljabar berdasarkan sifat-sifat perpangkatan Dengan demikian, jawaban yang tepat adalah E.

Pertidaksamaan tersebut dapat diselessaikan dengan melakukan manipulasi aljabar berdasarkan sifat-sifat perpangkatan

$table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses 1 third close parentheses to the power of 2 x plus 1 end exponent end cell greater than cell square root of 27 over 3 to the power of x minus 1 end exponent end root end cell row cell open parentheses 3 to the power of negative 1 end exponent close parentheses to the power of 2 x plus 1 end exponent end cell greater than cell open parentheses 3 cubed over 3 to the power of x minus 1 end exponent close parentheses to the power of 1 half end exponent end cell row cell 3 to the power of open parentheses negative 2 x minus 1 close parentheses end exponent end cell greater than cell open parentheses 3 to the power of 3 minus open parentheses x minus 1 close parentheses end exponent close parentheses to the power of 1 half end exponent end cell row cell 3 to the power of open parentheses negative 2 x minus 1 close parentheses end exponent end cell greater than cell open parentheses 3 to the power of 4 minus x end exponent close parentheses to the power of 1 half end exponent end cell row cell 3 to the power of open parentheses negative 2 x minus 1 close parentheses end exponent end cell greater than cell 3 to the power of open parentheses 2 minus x over 2 close parentheses end exponent end cell row cell negative 2 x minus 1 end cell greater than cell 2 minus x over 2 end cell row cell negative 2 x plus x over 2 end cell greater than cell 2 plus 1 end cell row cell negative fraction numerator 4 x over denominator 2 end fraction plus x over 2 end cell greater than 3 row cell negative fraction numerator 3 x over denominator 2 end fraction end cell greater than 3 row cell negative 3 x end cell greater than 6 row cell negative x end cell greater than cell 6 over 3 end cell row cell negative x end cell greater than 2 row x less than cell negative 2 end cell end table$

HP equals open curly brackets straight x vertical line straight x less than 2 close curly brackets

Dengan demikian, jawaban yang tepat adalah E.