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Penyelesaian pertidaksamaan  adalah ...

Pertanyaan

Penyelesaian pertidaksamaan 4 times 2 to the power of x squared plus 1 end exponent greater than open parentheses 1 half close parentheses to the power of 5 x plus 1 end exponent adalah ...

  1. x less than 1 space atau space x greater than 4 

  2. x less than negative 4 space atau space x greater than negative 1 

  3. x less than negative 5 space atau space x greater than 1 

  4. 1 less than x less than 4 

  5. negative 4 less than x less than negative 1  

Pembahasan Soal:

Diketahui:

Pertidaksamaan 4 times 2 to the power of x squared plus 1 end exponent greater than open parentheses 1 half close parentheses to the power of 5 x plus 1 end exponent

Ditanya:

Pernyelesaian pertidaksamaan tersebut.

Jika terdapat suatu pertidaksamaan dimana a greater than 1 dan a to the power of f open parentheses x close parentheses end exponent greater than a to the power of g left parenthesis x right parenthesis end exponent maka f open parentheses x close parentheses greater than g open parentheses x close parentheses.

Perlu diingat bahwa:

1 over k to the power of l equals k to the power of negative l end exponent k to the power of open parentheses l plus m close parentheses end exponent equals k to the power of l times k to the power of m open parentheses k to the power of l close parentheses to the power of m equals k to the power of l times m end exponent 

Perhatikan perhitungan berikut:

table attributes columnalign right center left columnspacing 0px end attributes row cell 4 times 2 to the power of x squared plus 1 end exponent end cell greater than cell open parentheses 1 half close parentheses to the power of 5 x plus 1 end exponent end cell row cell 2 squared times 2 to the power of x squared plus 1 end exponent end cell greater than cell open parentheses 2 to the power of negative 1 end exponent close parentheses to the power of 5 x plus 1 end exponent end cell row cell 2 to the power of x squared plus 1 plus 2 end exponent end cell greater than cell 2 to the power of negative 5 x minus 1 end exponent end cell row cell 2 to the power of x squared plus 3 end exponent end cell greater than cell 2 to the power of negative 5 x minus 1 end exponent end cell row cell x squared plus 3 end cell greater than cell negative 5 x minus 1 end cell row cell x squared plus 3 plus 5 x plus 1 end cell greater than cell negative 5 x plus 5 x minus 1 plus 1 end cell row cell x squared plus 5 x plus 4 end cell greater than 0 row cell open parentheses x plus 1 close parentheses open parentheses x plus 4 close parentheses end cell greater than 0 end table
table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open curly brackets table row cell x plus 1 greater than 0 rightwards arrow x greater than negative 1 end cell row cell x plus 4 greater than 0 rightwards arrow x greater than negative 4 end cell end table close end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open curly brackets table attributes columnalign left end attributes row cell x plus 1 less than 0 rightwards arrow x less than negative 1 end cell row cell x plus 4 less than 0 rightwards arrow x less than negative 4 end cell end table close end cell end table        

Irisan dari nilai x di atas:

x element of open parentheses negative 1 comma infinity close parentheses x element of open parentheses negative infinity comma negative 4 close parentheses

Gabungan irisan:

x element of open parentheses negative infinity comma negative 4 close parentheses union open parentheses negative 1 comma infinity close parentheses

Oleh sebab itu, didapat himpunan penyelesaiannya adalah open curly brackets x space left enclose space x less than negative 4 end enclose space atau space x greater than negative 1 close curly brackets.

Sehingga, penyelesaian pertidaksamaan 4 times 2 to the power of x squared plus 1 end exponent greater than open parentheses 1 half close parentheses to the power of 5 x plus 1 end exponent adalah x less than negative 4 space atau space x greater than negative 1.

Jadi, jawaban yang tepat adalah B.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 18 Juli 2021

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