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Semua nilai x yang memenuhi pertidaksamaan adalah...

Semua nilai x yang memenuhi pertidaksamaan x squared plus 2 x minus 3 greater than 0 space space d a n space open vertical bar 6 minus x close vertical bar greater than 3 x adalah...

  1. x less than negative 3 space a t a u space 0 less or equal than x less than 3 over 2

  2. x less than 3 over 2

  3. x less than negative 3 space a t a u space 1 less than x less than 3 over 2

  4. x less than negative 3 space a t a u space x greater than 3 over 2

  5. 0 less than x less than 3 over 2

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N. Rahayu

Master Teacher

Mahasiswa/Alumni Universitas Negeri Jakarta

Jawaban terverifikasi

Pembahasan

Pertidaksamaan yang pertama Buat garis bilangannya Soulusi untuk pertidaksamaan pertama : Pertidaksamaan yang kedua Gabungan solusi dari kedua pertidaksamaan, maka didapat:

Pertidaksamaan yang pertama

x squared plus 2 x minus 3 greater than 0 open parentheses x plus 3 close parentheses open parentheses x minus 2 close parentheses greater than 0 x equals negative 3 space a t a u space x equals 1

Buat garis bilangannya

Soulusi untuk pertidaksamaan pertama : open curly brackets x less than negative 3 space a t a u space x greater than 1 close curly brackets

Pertidaksamaan yang kedua

open vertical bar 6 minus x close vertical bar equals open curly brackets table row cell space space space space space space 6 minus x rightwards arrow u n t u k space x less or equal than 6 end cell row cell negative open parentheses 6 minus x close parentheses rightwards arrow u n t u k space x greater than 6 end cell end table close U n t u k space x less or equal than 6 6 minus x greater than 3 x minus 4 x greater than negative 6 rightwards arrow b a g i space d e n g a n minus 4 space space space space space space x less than 6 over 4 space space space space space space x less than 6 over 4 U n t u k space x greater than 6 minus left parenthesis 6 minus x right parenthesis greater than 3 x space space space space space space space space space space space space space space x minus 6 greater than 3 x space space space space space space space space space space space space space space space space minus 2 x greater than 6 rightwards arrow b a g i space d e n g a n minus 2 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 than negative 3

Gabungan solusi dari kedua pertidaksamaan, maka didapat:

equals open curly brackets x less than negative 3 space a t a u space x greater than 1 close curly brackets space d a n space open curly brackets x less than 3 over 2 close curly brackets equals open curly brackets x less than negative 3 close curly brackets space a t a u space open curly brackets 1 less than x less than 3 over 2 close curly brackets

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