Question

7.Решите уравнения: 1) ( х+1)/12 -1=(2х+3)/4
2) 2(х-6)+4х=5х-(8-х)
3) (5у+1)/4+(3у+2)/16=3
4) 5(х-2)+3х=2х-(10-6х)

Answer 1

Ответ:

$1) \frac{x+1}{12} - 1 = \frac{2x+3}{4}\\\\\frac{x+1-12}{12} = \frac{2x+3}{4}\\\\    \frac{x-11}{12} = \frac{3(2x+3)}{12}\\\\x - 11 = 6x + 9\\\\x - 6x = 9 + 11\\\\-5x = 20\\\\x = -4$

$2) 2(x-6)+4x=5x-(8-x)\\\\2x - 12 + 4x = 5x - 8 + x\\\\2x + 4x - 5x - x = -8 + 12\\\\0x = 4\\\\x \in \varnothing$

$3) \frac{5y+1}{4} + \frac{3y+2}{16} =3\\\\4(5y+1) + 3y+2 = 48\\\\20y + 4 + 3y + 2 = 48\\\\20y + 3y = 48 - 4 - 2\\\\23y = 42\\\\y = \frac{42}{23} = 1\frac{19}{23}$

$4) 5(x-2) + 3x = 2x - (10 - 6x)\\\\5x - 10 + 3x = 2x - 10 + 6x\\\\5x + 3x - 2x - 6x = -10 + 10\\\\0x = 0\\\\x \in R$