Question

Решите подробно уравнение!
1) (х-5):0,7=(2х-9):0,4
2) х:(3,8-х)=х:(5,6-3х)
3) х:7 1/3=6:1,1

Answer 1

$1 \ frac{x-5}{0.7}= frac{2x-9}{0.4} \ 0.4(x-5)=0.7(2x-9) \ 0.4x-2=1.4x-6.3 \ 0.4x-1.4x=-6.3+2 \ -x=-4.3 \ x=4.3$

$2 \ frac{x}{3.8-x}= frac{x}{5.6-3x} \ 3.8-x neq 0; 5.6-3x neq 0; x neq 3.8; x neq frac{28}{15} \ x(5.6-3x)=x(3.8-x) \ 5.6x-3 x^{2} =3.8x- x^{2} \ 5.6x-3 x^{2} -3.8x+ x^{2} =0 \ -2 x^{2} +1.8x=0 \ x^{2} -0.9x=0 \ x(x-0.9)=0 \ x_1=0 \ x_2=0.9$

$3 \ frac{x}{7 frac{1}{3} }= frac{6}{1.1} \ x=6*7 frac{1}{3}:1.1 \ x= frac{6}{1}* frac{22}{3}* frac{10}{11} \ x= 40$

Answer 2

$1) 0.7*(2x-9)=0.4*(x-5) \ 1.4x-6.3=0.4x-2 \ 1.4x-0.4x=6.3-2 \ x=4.3 \ \ 2) x*(3.8-x)=x*(5.6-3x) \ 3.8x-x^2=5.6x-3x^2 \ -2x^2+5.6x-3.8x=0 \ -2x^2+1.8x=0\ -x^2+0.9x=0 \ -x(x-0.9)=0 \ x=0 \ x=0.9 \ \ 3)1.1x=6* frac{22}{3} \ 1.1x=44 \ x=40$