Iklan

Iklan

Pertanyaan

4 x 2 + 2 x − 6 2 x 2 + 5 x − 3 ​ < 0 berlaku untuk ...

 berlaku untuk ...

  1. negative 1 half less than x less than 1

  2. negative 3 less than x less than 0

  3. negative 3 less than x less than negative 3 over 2 atau 1 half less than x less than 1

  4. x less than negative 3 atau x greater than 3 over 2

  5. x greater than 3 over 2

Iklan

S. Ayu

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Prof. DR. Hamka

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah C.

jawaban yang tepat adalah C.

Iklan

Pembahasan

Bentuk umum pertidaksamaan rasional: Fungsi . Pembuat nol: Pembilang Penyebut Syarat: Uji titik: Untuk interval , ambil titik . Untuk interval , ambil titik . Untuk interval , ambil titik . Untuk interval , ambil titik . Untuk interval , ambil titik . Garis bilangan: Karena pertidaksamaan bertanda " ", maka daerah penyelesaian berada pada interval yang bertanda atau bernilai megatif. berlaku untuk atau . Jadi, jawaban yang tepat adalah C.

Bentuk umum pertidaksamaan rasional:

fraction numerator f open parentheses x close parentheses over denominator g open parentheses x close parentheses end fraction less than 0 semicolon space g open parentheses x close parentheses not equal to 0

Fungsi fraction numerator 2 x squared plus 5 x minus 3 over denominator 4 x squared plus 2 x minus 6 end fraction less than 0.

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 2 x squared plus 5 x minus 3 over denominator 4 x squared plus 2 x minus 6 end fraction end cell less than 0 row cell fraction numerator 2 x squared plus 6 x minus x minus 3 over denominator 2 open parentheses 2 x squared plus x minus 3 close parentheses end fraction end cell less than 0 row cell fraction numerator 2 x open parentheses x plus 3 close parentheses minus open parentheses x plus 3 close parentheses over denominator 2 open parentheses 2 x squared plus 3 x minus 2 x minus 3 close parentheses end fraction end cell less than 0 row cell fraction numerator open parentheses 2 x minus 1 close parentheses open parentheses x plus 3 close parentheses over denominator 2 open parentheses x open parentheses 2 x plus 3 close parentheses minus open parentheses 2 x plus 3 close parentheses close parentheses end fraction end cell less than 0 row cell fraction numerator open parentheses 2 x minus 1 close parentheses open parentheses x plus 3 close parentheses over denominator 2 open parentheses x minus 1 close parentheses open parentheses 2 x plus 3 close parentheses end fraction end cell less than 0 end table

Pembuat nol:

  • Pembilang

table attributes columnalign right center left columnspacing 0px end attributes row cell 2 x minus 1 end cell equals 0 row cell 2 x end cell equals 1 row x equals cell 1 half end cell row blank blank blank row cell x plus 3 end cell equals 0 row x equals cell negative 3 end cell end table

  • Penyebut

table attributes columnalign right center left columnspacing 0px end attributes row cell x minus 1 end cell equals 0 row x equals 1 row blank blank blank row cell 2 x plus 3 end cell equals 0 row cell 2 x end cell equals cell negative 3 end cell row x equals cell negative 3 over 2 end cell end table

Syarat:

table attributes columnalign right center left columnspacing 0px end attributes row cell x minus 1 end cell not equal to 0 row x not equal to 1 row blank blank blank row cell 2 x plus 3 end cell not equal to 0 row cell 2 x end cell not equal to cell negative 3 end cell row x not equal to cell negative 3 over 2 end cell end table

Uji titik:

Untuk interval x less than negative 3, ambil titik x equals negative 4.

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 2 x squared plus 5 x minus 3 over denominator 4 x squared plus 2 x minus 6 end fraction end cell equals cell fraction numerator 2 open parentheses negative 4 close parentheses squared plus 5 open parentheses negative 4 close parentheses minus 3 over denominator 4 open parentheses negative 4 close parentheses squared plus 2 open parentheses negative 4 close parentheses minus 6 end fraction end cell row blank equals cell fraction numerator 2 open parentheses 16 close parentheses minus 20 minus 3 over denominator 4 open parentheses 16 close parentheses minus 8 minus 6 end fraction end cell row blank equals cell fraction numerator 32 minus 23 over denominator 64 minus 14 end fraction end cell row blank equals cell 9 over 50 space open parentheses plus close parentheses end cell end table

Untuk interval negative 3 less than x less than negative 3 over 2, ambil titik x equals negative 2.

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 2 x squared plus 5 x minus 3 over denominator 4 x squared plus 2 x minus 6 end fraction end cell equals cell fraction numerator 2 open parentheses negative 2 close parentheses squared plus 5 open parentheses negative 2 close parentheses minus 3 over denominator 4 open parentheses negative 2 close parentheses squared plus 2 open parentheses negative 2 close parentheses minus 6 end fraction end cell row blank equals cell fraction numerator 2 open parentheses 4 close parentheses minus 10 minus 3 over denominator 4 open parentheses 4 close parentheses minus 4 minus 6 end fraction end cell row blank equals cell fraction numerator 8 minus 13 over denominator 16 minus 10 end fraction end cell row blank equals cell negative 5 over 6 space open parentheses minus close parentheses end cell end table

Untuk interval negative 3 over 2 less than x less than 1 half, ambil titik x equals 0.

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 2 x squared plus 5 x minus 3 over denominator 4 x squared plus 2 x minus 6 end fraction end cell equals cell fraction numerator 2 open parentheses 0 close parentheses squared plus 5 open parentheses 0 close parentheses minus 3 over denominator 4 open parentheses 0 close parentheses squared plus 2 open parentheses 0 close parentheses minus 6 end fraction end cell row blank equals cell fraction numerator 0 plus 0 minus 3 over denominator 0 plus 0 minus 6 end fraction end cell row blank equals cell fraction numerator negative 3 over denominator negative 6 end fraction end cell row blank equals cell 1 half space open parentheses plus close parentheses end cell end table

Untuk interval 1 half less than x less than 1, ambil titik x equals 2 over 3.

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 2 x squared plus 5 x minus 3 over denominator 4 x squared plus 2 x minus 6 end fraction end cell equals cell fraction numerator 2 open parentheses begin display style 2 over 3 end style close parentheses squared plus 5 open parentheses begin display style 2 over 3 end style close parentheses minus 3 over denominator 4 open parentheses begin display style 2 over 3 end style close parentheses squared plus 2 open parentheses begin display style 2 over 3 end style close parentheses minus 6 end fraction end cell row blank equals cell fraction numerator 2 open parentheses begin display style 4 over 9 end style close parentheses plus begin display style 10 over 3 end style minus 3 over denominator 4 open parentheses begin display style 4 over 9 end style close parentheses plus begin display style 4 over 3 end style minus 6 end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator 8 over denominator down diagonal strike 9 end fraction end style plus begin display style fraction numerator 30 over denominator down diagonal strike 9 end fraction end style minus begin display style fraction numerator 27 over denominator down diagonal strike 9 end fraction end style over denominator begin display style fraction numerator 16 over denominator down diagonal strike 9 end fraction end style plus begin display style fraction numerator 12 over denominator down diagonal strike 9 end fraction end style minus begin display style fraction numerator 54 over denominator down diagonal strike 9 end fraction end style end fraction end cell row blank equals cell fraction numerator 8 plus 30 minus 27 over denominator 16 plus 12 minus 54 end fraction end cell row blank equals cell fraction numerator 11 over denominator negative 26 end fraction end cell row blank equals cell negative 11 over 26 space open parentheses minus close parentheses end cell end table

Untuk interval x greater than 1, ambil titik x equals 2.

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 2 x squared plus 5 x minus 3 over denominator 4 x squared plus 2 x minus 6 end fraction end cell equals cell fraction numerator 2 open parentheses 2 close parentheses squared plus 5 open parentheses 2 close parentheses minus 3 over denominator 4 open parentheses 2 close parentheses squared plus 2 open parentheses 2 close parentheses minus 6 end fraction end cell row blank equals cell fraction numerator 2 open parentheses 4 close parentheses plus 10 minus 3 over denominator 4 open parentheses 4 close parentheses plus 4 minus 6 end fraction end cell row blank equals cell fraction numerator 8 plus 7 over denominator 16 minus 2 end fraction end cell row blank equals cell 15 over 14 space open parentheses plus close parentheses end cell end table

Garis bilangan:

Karena pertidaksamaan bertanda "less than", maka daerah penyelesaian berada pada interval yang bertanda open parentheses minus close parentheses atau bernilai megatif.

fraction numerator 2 x squared plus 5 x minus 3 over denominator 4 x squared plus 2 x minus 6 end fraction less than 0 berlaku untuk negative 3 less than x less than negative 3 over 2 atau 1 half less than x less than 1.

Jadi, jawaban yang tepat adalah C.

Perdalam pemahamanmu bersama Master Teacher
di sesi Live Teaching, GRATIS!

2

Iklan

Iklan

Pertanyaan serupa

Penyelesaian daripertidaksamaan x x 2 + 2 ​ ≥ 3 adalah ....

5

1.0

Jawaban terverifikasi

RUANGGURU HQ

Jl. Dr. Saharjo No.161, Manggarai Selatan, Tebet, Kota Jakarta Selatan, Daerah Khusus Ibukota Jakarta 12860

Coba GRATIS Aplikasi Roboguru

Coba GRATIS Aplikasi Ruangguru

Download di Google PlayDownload di AppstoreDownload di App Gallery

Produk Ruangguru

Hubungi Kami

Ruangguru WhatsApp

+62 815-7441-0000

Email info@ruangguru.com

info@ruangguru.com

Contact 02140008000

02140008000

Ikuti Kami

©2024 Ruangguru. All Rights Reserved PT. Ruang Raya Indonesia