Решите уравнение:
\({\largeа)}\ 3(5x-4)-8x=4x+9;\)
\({\largeб)}\ 19x-8(x-3)=66-3x;\)
\({\largeв)}\ 0{,}2(0{,}7x-5)+0{,}02=1{,}4(x-1{,}6);\)
\({\largeг)}\ 2{,}7(0{,}1x+3{,}2)+0{,}6(1{,}3-x)=16{,}02.\)
Упражнение 72
Источник заимствования: Математика. Алгебра. 8 класс. Базовый уровень. / Ю.Н. Макарычев, Н.Г. Миндюк, К.И. Нешков, С.Б. Суворова – Просвещение, 2023. – 22 c. ISBN 978-5-09-102536-1
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Решение:
\({\largeа)}\ 3(5x-4)-8x=4x+9\)
\(\phantom{\largeа)}\ 15x-12-8x=4x+9\)
\(\phantom{\largeа)}\ 15x-8x-4x=9+12\)
\(\phantom{\largeа)}\ 3x=21\)
\(\phantom{\largeа)}\ x=21:3\)
\(\phantom{\largeа)}\ x=7\)
\(\phantom{\largeа)}\ 15x-12-8x=4x+9\)
\(\phantom{\largeа)}\ 15x-8x-4x=9+12\)
\(\phantom{\largeа)}\ 3x=21\)
\(\phantom{\largeа)}\ x=21:3\)
\(\phantom{\largeа)}\ x=7\)
\({\largeб)}\ 19x-8(x-3)=66-3x\)
\(\phantom{\largeб)}\ 19x-8x+24=66-3x\)
\(\phantom{\largeб)}\ 19x-8x+3x=66-24\)
\(\phantom{\largeб)}\ 14x=42\)
\(\phantom{\largeб)}\ x=42:14\)
\(\phantom{\largeб)}\ x=3\)
\(\phantom{\largeб)}\ 19x-8x+24=66-3x\)
\(\phantom{\largeб)}\ 19x-8x+3x=66-24\)
\(\phantom{\largeб)}\ 14x=42\)
\(\phantom{\largeб)}\ x=42:14\)
\(\phantom{\largeб)}\ x=3\)
\({\largeв)}\ 0{,}2(0{,}7x-5)+0{,}02=1{,}4(x-1{,}6)\)
\(\phantom{\largeв)}\ 0{,}14x-1+0{,}02=1{,}4x-2{,}24\)
\(\phantom{\largeв)}\ 1{,}4x-0{,}14x=2{,}24-1+0{,}02\)
\(\phantom{\largeв)}\ 1{,}26x=1{,}26\)
\(\phantom{\largeв)}\ x=1{,}26:1{,}26\)
\(\phantom{\largeв)}\ x=1\)
\(\phantom{\largeв)}\ 0{,}14x-1+0{,}02=1{,}4x-2{,}24\)
\(\phantom{\largeв)}\ 1{,}4x-0{,}14x=2{,}24-1+0{,}02\)
\(\phantom{\largeв)}\ 1{,}26x=1{,}26\)
\(\phantom{\largeв)}\ x=1{,}26:1{,}26\)
\(\phantom{\largeв)}\ x=1\)
\({\largeг)}\ 2{,}7(0{,}1x+3{,}2)+0{,}6(1{,}3-x)=16{,}02\)
\(\phantom{\largeг)}\ 0{,}27x+8{,}64+0{,}78-0{,}6x=16{,}02\)
\(\phantom{\largeг)}\ 0{,}27x-0{,}6x=16{,}02-8{,}64-0{,}78\)
\(\phantom{\largeг)}\ {-}0{,}33x=6{,}6\)
\(\phantom{\largeг)}\ x=6{,}6:({-}0{,}33)\)
\(\phantom{\largeг)}\ x=660:({-}33)\)
\(\phantom{\largeг)}\ x={-}20\)
\(\phantom{\largeг)}\ 0{,}27x+8{,}64+0{,}78-0{,}6x=16{,}02\)
\(\phantom{\largeг)}\ 0{,}27x-0{,}6x=16{,}02-8{,}64-0{,}78\)
\(\phantom{\largeг)}\ {-}0{,}33x=6{,}6\)
\(\phantom{\largeг)}\ x=6{,}6:({-}0{,}33)\)
\(\phantom{\largeг)}\ x=660:({-}33)\)
\(\phantom{\largeг)}\ x={-}20\)