Pertanyaan

Jika x bilangan bulat, tentukan himpunan penyelesaian dari pertidaksamaan berikut a. 2 ( 2 x − 1 ) < 3 ( 2 x + 2 )

Jika $x$ bilangan bulat, tentukan himpunan penyelesaian dari pertidaksamaan berikut

a. $2 (2 x - 1) < 3 (2 x + 2)$

Ikuti Tryout SNBT & Menangkan E-Wallet 100rb

Habis dalam

Klaim

D. Rajib

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Malang

Jawaban terverifikasi

Jawaban

himpunan penyelesaian dari pertidaksamaan tersebut adalah HP = { x ∣ x > − 4 , x ∈ bilangan bulat } .

himpunan penyelesaian dari pertidaksamaan tersebut adalah

HP = {x ∣ x > - 4, x \in bilangan bulat}

Pembahasan

Kita dapat menyelesaikan pertidaksamaan linear satu variabel dengan cara menambah, mengurang, mengali, atau membagi kedua ruas dengan bilangan yang sama. Khusus untuk perkalian dan pembagian kedua ruas dengan bilangan negatif, tanda pertidaksamaannya berubah/dibalik. Ingat kembali sifat distributif a ( b + c ) = ab + a c Perhatikan perhitungan berikut! &\frac8{{\color[rgb]{0.0, 0.0, 1.0}-}{\color[rgb]{0.0, 0.0, 1.0}2}}\\x&>&-4\end{array}" data-mathml="«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mtable columnspacing=¨0px¨ columnalign=¨right center left¨»«mtr»«mtd»«mn»2«/mn»«mfenced»«mrow»«mn»2«/mn»«mi»x«/mi»«mo»-«/mo»«mn»1«/mn»«/mrow»«/mfenced»«/mtd»«mtd»«mo»§#60;«/mo»«/mtd»«mtd»«mn»3«/mn»«mfenced»«mrow»«mn»2«/mn»«mi»x«/mi»«mo»+«/mo»«mn»2«/mn»«/mrow»«/mfenced»«/mtd»«/mtr»«mtr»«mtd»«mn»4«/mn»«mi»x«/mi»«mo»-«/mo»«mn»2«/mn»«/mtd»«mtd»«mo»§#60;«/mo»«/mtd»«mtd»«mn»6«/mn»«mi»x«/mi»«mo»+«/mo»«mn»6«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»4«/mn»«mi»x«/mi»«mo»-«/mo»«mn»2«/mn»«mo»+«/mo»«mn mathcolor=¨#0000FF¨»2«/mn»«/mtd»«mtd»«mo»§#60;«/mo»«/mtd»«mtd»«mn»6«/mn»«mi»x«/mi»«mo»+«/mo»«mn»6«/mn»«mo»+«/mo»«mn mathcolor=¨#0000FF¨»2«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»4«/mn»«mi»x«/mi»«/mtd»«mtd»«mo»§#60;«/mo»«/mtd»«mtd»«mn»6«/mn»«mi»x«/mi»«mo»+«/mo»«mn»8«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»4«/mn»«mi»x«/mi»«mo»-«/mo»«mn mathcolor=¨#0000FF¨»6«/mn»«mi mathcolor=¨#0000FF¨»x«/mi»«/mtd»«mtd»«mo»§#60;«/mo»«/mtd»«mtd»«mn»6«/mn»«mi»x«/mi»«mo»+«/mo»«mn»8«/mn»«mo»-«/mo»«mn mathcolor=¨#0000FF¨»6«/mn»«mi mathcolor=¨#0000FF¨»x«/mi»«/mtd»«/mtr»«mtr»«mtd»«mo»-«/mo»«mn»2«/mn»«mi»x«/mi»«/mtd»«mtd»«mo»§#60;«/mo»«/mtd»«mtd»«mn»8«/mn»«/mtd»«/mtr»«mtr»«mtd»«mfrac»«mrow»«mo»-«/mo»«mn»2«/mn»«mi»x«/mi»«/mrow»«mrow»«mo mathcolor=¨#0000FF¨»-«/mo»«mn mathcolor=¨#0000FF¨»2«/mn»«/mrow»«/mfrac»«/mtd»«mtd»«mo»§#62;«/mo»«/mtd»«mtd»«mfrac»«mn»8«/mn»«mrow»«mo mathcolor=¨#0000FF¨»-«/mo»«mn mathcolor=¨#0000FF¨»2«/mn»«/mrow»«/mfrac»«/mtd»«/mtr»«mtr»«mtd»«mi»x«/mi»«/mtd»«mtd»«mo»§#62;«/mo»«/mtd»«mtd»«mo»-«/mo»«mn»4«/mn»«/mtd»«/mtr»«/mtable»«/math»" role="math" src="data:image/png;base64,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" style="max-width: none;"> Dengan demikian, himpunan penyelesaian dari pertidaksamaan tersebut adalah HP = { x ∣ x > − 4 , x ∈ bilangan bulat } .

Kita dapat menyelesaikan pertidaksamaan linear satu variabel dengan cara menambah, mengurang, mengali, atau membagi kedua ruas dengan bilangan yang sama. Khusus untuk perkalian dan pembagian kedua ruas dengan bilangan negatif, tanda pertidaksamaannya berubah/dibalik.

Ingat kembali sifat distributif

$a (b + c) = ab + a c$

Perhatikan perhitungan berikut!

$table attributes columnalign right center left columnspacing 0px end attributes row cell 2 open parentheses 2 x minus 1 close parentheses end cell less than cell 3 open parentheses 2 x plus 2 close parentheses end cell row cell 4 x minus 2 end cell less than cell 6 x plus 6 end cell row cell 4 x minus 2 plus 2 end cell less than cell 6 x plus 6 plus 2 end cell row cell 4 x end cell less than cell 6 x plus 8 end cell row cell 4 x minus 6 x end cell less than cell 6 x plus 8 minus 6 x end cell row cell negative 2 x end cell less than 8 row cell fraction numerator negative 2 x over denominator negative 2 end fraction end cell greater than cell fraction numerator 8 over denominator negative 2 end fraction end cell row x greater than cell negative 4 end cell end table$

Dengan demikian, himpunan penyelesaian dari pertidaksamaan tersebut adalah $HP = {x ∣ x > - 4, x \in bilangan bulat}$ .