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

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

Answer 2

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

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

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