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Aljabar-Matematika



Kata aljabar adalah variasi kata arab "aljabr" yang kira-kira berarti
sebuah reuni atau penggabungan bagian-bagian, artinya aljabar membahas
tentang hubungan, yaitu hubungan antar-bilangan atau antar suku dalam
sebuah persamaan.

Aljabar merupakan cabang matematika yang pertama kali ditemukan oleh
Al-Khawarismi. Kitabnya yang berjudul Hisabul Jabarwal Muqabalah (The
mathematic of integration and equation) adalah buku pertama atau
tertua bidang aljabar. Geral of cremona menerjemahkan buku ini dan
memasukkan aljabar ke Eropa hingga menjadi referensi utama di bidang
aljabar pada universitas abad 19. Atas jasa-jasanya Al-Khwarismi
digelari sebagai "Bapak Aljabar".

Sebelum aljabar muncul, soal-soal aritmatika sulit untuk
disederhanakan. Keberadaan Aljabar adalah sebagai sebuah cara untuk
menyederhanakan soal dan mengeneralisasi aritmatika. Misalkan dalam
sebuah soal yang ditulis oleh Ahmes (Ahli Tulis Mesir) dalam Rhind
Papyrus, " Berapakah aha jika aha ditambah aha pertujuh samadengan 19
? Itu tidak lain adalah persoalan aljabar yang secara matematisnya
ditulis
x+(x/7) =19.

Bilangan adalah dasar dari pekerjaan aljabar, pembentuk dasar aljabar
yang memberikan sebuah nilai untuk dikerjakan. Bilangan-bilangan
tersebut diwakili oleh suatu huruf yang mengartikan bahwa bilangan
tersebut belum diketahui nilainya yang akan diselesaikan, penyeesaian
tersebut adalah sebuah nilai yang memenuhi pernyataan aljabarnya.
Bilangan yang diwakili dengan huruf tersebut dinamakan peubah atau
variabel. Peubah yang sering digunakan yaitu n (number) dan x (huruf
misteri). Contoh 2x+4, merupakan bentuk aljabar yang menunjukkan
gabungan antara nilai dan operasi yang bisa digunakan untuk
menunjukkan bagaimana keduanya saling berkaitan dan saling
membandingkan.

Bentuk aljabar tersebut, 2x+4 terdiri atas dua suku yaitu 2x dan 4.
Suku adalah pengelompokkan satu faktor (peubah dan/atau variabel),
sehingga penjumlahan/pengurangan akan memisahkan suku-suku yang ada.
Sebaliknya perkalian merupakan salah satu hal yang menghubungkan
bilangan dengan peubah.

Dalam aljabar dibicarakan mengenai,
- Bentuk Aljabar;
- Suku
- Persamaan
- Operasi
- Peubah
- Konstanta, dan
- Pangkat

Dari persamaan yang ada aljabar diatur untuk menyederhanakan,
memfaktorkan, dan menyelesaikan persamaan tesebut. Contoh:

x+ (x/7)=19
Untuk menyederhanakan kalikan kedua ruas masing-masing dengan 7,
sehingga mendapatkan bentuk yang equivalen(<=>):

7.x + 7.(x/7) = 19.7
<=> 7x + x =133

Dengan cara memfaktorkan ruas kiri diperoleh :

(7+1)x=133
8x=133

Untuk menyelesaikan, masing-masing kedua ruas di kali dengan 1/8 atau
dengan kata lain dibagi 8 , seperti dibawah !

(1/8).8x=(1/8).133
(8/8).x=133/8
x=133/8
jadi diperoleh penyelesaian x=133/8.

Dari pembahasan di atas, bahasan dalam aljabar adalah menggunakan
sebuah peubah untuk mewakili sebuah nilai, kemudian memasukannya ke
dalam beberapa operasi dan kemudian menggunakan beberapa aturan khusus
seperti peragaan soal di atas, yang telah ditetapkan dan mempunyai
sistem yang telah terorganisasi dengan baik untuk menyederhanakan,
menyelesaikan, membandingkan, atau menetapkan suatu persamaan.

Referensi:
Aljabar Dumies
Wikepedia

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