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Logika Menyelesaikan Persamaan



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http://matematikakubisa.blogspot.com/2014/03/aljabar-matematika.html

Logika Menyelesaikan Persamaan Linear baik PLSV atau PLDV, Persamaan
Kuadrat, atau apa saja hakikatnya adalah sama yaitu untuk mencari
SOLUSI dari persamaan. Solusi yaitu himpunan penyelesaian yang membuat
persamaan berlaku. Himpunan Penyelesaian yang ada dalam suatu
persamaan adalah tunggal, banyak atau tak berhingga, dan tak punya
penyelesaian.

Persamaan adalah kalimat terbuka matematika yang dihubungkan dengan
tanda sama dengan (=). Kalimat terbuka adalah kalimat yang belum
diketahui nilai kebenarannya.

Contoh: Kalimat "Jakarta adalah ibu kota Indonesia" merupakan kalimat
tertutup karena telah diketahui nilai kebenarannya. Nilai kebenaran
pada kalimat tertutup bisa bernilai benar dan bisa bernilai salah
tetapi tidak keduanya sekaligus.

2x+2=4
apakah kalimat terbuka atau tidak ? Jawabannya ialah Kalimat terbuka
karena nilai kebenarannya belum diketahui benar atau salah. Kalimat
terbuka matematika dalam persamaan ditandai dengan adanya suatu nilai
yang berupa variabel atau peubah. Untuk mencari nilai apa yang cocok
untuk digantikan pada contoh persamaan di atas, sehingga di diperoleh
suatu solusi yang menyebabkan persamaannya berlaku atau dengan kata
lain bernilai benar maka dilakukan dengan suatu cara tertentu. Proses
pencarian nilai itulah yang dimaksud dengan Menyelesaikan Persamaan,
mencari solusi atau himpunan penyelesaian sehingga persamaannya
berlaku (bernilai benar).

Bagaimana mencari solusi dari suatu persamaan ?

Seperti kasus soal di atas 2x+2=4, berapakah nilai x sehingga
persamaannya berlaku (bernilai benar). Jika kita menguji x=0 dan
memasukkannya ke dalam persamaan tersebut maka 2(0)+2=2 bukan 4.
Olehnya itu, 0 bukan solusi dari persamaan 2x+2=4 melainkan 1 adalah
solusi dari persamaan tersebut.

Memahami konsep matematika apa yang ada dalam suatu persamaan menjadi
faktor utama sehingga kita mampuh menyelesaikan suatu persamaan yang
ada. Khusunya operasi seperti +, -, x, : , pangkat, logaritma dan
lain-lain. Selain itu juga, kita perluh memahami dan dapat merubah
persamaan ke bentuk lain yang ekuivalen. Persamaan yang ekuivalen
adalah persamaan yang mempunyai himpunan penyelesaian yang sama.

Contoh: X+1=3 ekuivalen dengan 2X+2=6 karena memiliki himpunan penyelesaian x=2.

Artikel Penunjang yang Berkaitan dengan "Logika Menyelesaikan Persamaan"

¤Menyelesaikan Persamaan Linear Satu Variabel (PLSV)
¤Menyelesaikan Persamaan Linear Dua Variabel (PLDV)
¤Menyelesaikan Persamaan Kuadrat
¤Solusi Tunggal, Banyak, dan kosong
¤Merubah Persamaan Ke Persamaan Lain yang Ekuivalen
¤Simbol-Simbol Matematika
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