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Himpunan penyelesaian dari pertidaksamaan (31​)2x+1>3x−127​​ adalah ...

Pertanyaan

Himpunan penyelesaian dari pertidaksamaan open parentheses 1 third close parentheses to the power of 2 x plus 1 end exponent greater than square root of 27 over 3 to the power of x minus 1 end exponent end root adalah ...

  1. x greater than 5 over 6 

  2. x less than negative 6 over 5 

  3. x greater than negative 5 over 6 

  4. x less than 2 

  5. x less than negative 2 

B. Hary

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah E.

Pembahasan

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.

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