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Selesaikan.  −1−x​≥x+3

Pertanyaan

Selesaikan. 

square root of negative 1 minus x end root greater or equal than x plus 3 

L. Marlina

Master Teacher

Mahasiswa/Alumni Institut Teknologi Bandung

Jawaban terverifikasi

Jawaban

himpunan penyelesaian adalah H p equals open curly brackets x vertical line minus 3 less or equal than x less or equal than negative 2 close curly brackets.

Pembahasan

Pertidaksamaan tersebut merupakan pertidaksamaan irasional, syaratnya yang di dalam akar lebih dari atau sama dengan nol. Dan hasil akar tidak negatif. Maka, syaratanya ada dua, yaitu:

open parentheses i close parentheses space minus 1 minus x greater or equal than 0 space space space space space space space space space space space space space space space space space space open parentheses i i close parentheses space x plus 3 greater or equal than 0 space space space space space space space space space space space minus x greater or equal than 1 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space x greater or equal than negative 3 space space space space space space space space space space space space space space x less or equal than negative 1 

Untuk menyelesaiakan pertidaksamaan tersebut bisa kita kuadratkan kedua ruas,

space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space open parentheses square root of negative 1 minus x end root close parentheses squared greater or equal than open parentheses x plus 3 close parentheses squared space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space open parentheses negative 1 minus x close parentheses squared greater or equal than open parentheses x plus 3 close parentheses squared space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space open parentheses negative 1 minus x close parentheses squared minus open parentheses x plus 3 close parentheses squared greater or equal than 0 open parentheses open parentheses negative 1 minus x close parentheses minus open parentheses x plus 3 close parentheses close parentheses open parentheses open parentheses negative 1 minus x close parentheses plus open parentheses x plus 3 close parentheses close parentheses greater or equal than 0 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space open parentheses negative 2 x minus 4 close parentheses open parentheses 2 close parentheses greater or equal than 0 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space open parentheses negative 2 x minus 4 close parentheses greater or equal than 0 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space x plus 2 less or equal than 0 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space x less or equal than negative 2 

Penyelesaian yang kita peroleh adalah x less or equal than negative 2. Kemudian, kita iriskan dengan syaratnya yaitu x less or equal than negative 1 dan x greater or equal than negative 3. Maka, irisanya adalah 

negative 3 less or equal than x less or equal than negative 2 

Jadi, himpunan penyelesaian adalah H p equals open curly brackets x vertical line minus 3 less or equal than x less or equal than negative 2 close curly brackets.

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