Question

[ Repede va rog ] Determinati numarul necunoscut pentru fiecare dintre urmatoarele proportii:
a) x+1/5 = 4/13;
b)x-2/x = 7/13;
c) 3x+4/x+5 = 5/3;
d)4x-3/11 = 2x+5/7;
e)x+1/0. 5 = 2x+8=4:
f) x/1/3 = 0,(7)/2/3;
g) (1/5+3/4/) /x = 3/20.

Answer 1

Răspuns:

* - inmultire

Explicație pas cu pas:

a)$\frac{x+1}{5} =\frac{4}{13}$, inmultim pe diagonala

$(x+1) * 13= 5*4\\13x+13=20|-13\\13x=7$

$x=\frac{7}{13}$

b) $\frac{x-2}{x} =\frac{7}{13}$, inmultim pe diagonala

$(x-2)*13= x*7\\13x-26=7x\\13x-7x=26\\6x=26|:6\\x=\frac{26}{6}\\x=\frac{13}{2}$

c) $\frac{3x+4}{x+5} =\frac{5}{3}$, inmultim pe diagonala

$(3x+4)*3=(x+5)*5\\9x+12=5x+25\\9x-5x=25-12\\4x=13|:4\\x=\frac{13}{4}$

d)$\frac{4x-3}{11} =\frac{2x+5}{7}$, inmultim pe diagonala

$(4x-3)*7=(2x+5)*11\\28x-21=22x+55\\28x-22x=55+21\\6x=76|:6\\x=\frac{76}{6} \\x=\frac{38}{3}$

e)$\frac{x+1}{0.5} =\frac{2x+8}{4}$, inmultim pe diagonala

$(x+1)*4=(2x+8)*0.5\\4x+4= x+4\\4x-x=4-4\\3x=0|:3\\x=0$

f)$\frac{x}{1} /\frac{3}{1} =\frac{0,(7)}{2} /\frac{3}{1}$

$\frac{x}{1} *\frac{1}{3} =\frac{0,(7)}{2} *\frac{1}{3}$

$\frac{x}{3} =\frac{0,(7)}{6}$, inmultim pe diagonala

$x*6= 3*0,(7)\\6x=3*\frac{7}{9} \\6x=\frac{7}{3}|:6\\x= \frac{7}{3} : \frac{6}{1} \\x= \frac{7}{1} : \frac{3}{1} \\x= \frac{7}{1} *\frac{1}{3}\\x= \frac{7}{3}$

g)$\frac{1/5+3/4}{x} =\frac{3}{20}$, inmultim pe diagonala

$(1/5+3/4)*20=3*x$, in paranteza prima amplificam cu 4 si a doua cu 5

$(4+15/20)*20=3x\\\frac{19}{20}*20 =3x$

$3x=19|:3\\x=\frac{19}{3}$