[ 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.

Răspuns:

* - inmultire

Explicație pas cu pas:

a)[tex]\frac{x+1}{5} =\frac{4}{13}[/tex], inmultim pe diagonala

[tex](x+1) * 13= 5*4\\13x+13=20|-13\\13x=7\\\\[/tex]

[tex]x=\frac{7}{13}[/tex]

b) [tex]\frac{x-2}{x} =\frac{7}{13} \\[/tex], inmultim pe diagonala

[tex](x-2)*13= x*7\\13x-26=7x\\13x-7x=26\\6x=26|:6\\x=\frac{26}{6}\\x=\frac{13}{2}[/tex]

c) [tex]\frac{3x+4}{x+5} =\frac{5}{3}[/tex], inmultim pe diagonala

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

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

[tex](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}[/tex]

e)[tex]\frac{x+1}{0.5} =\frac{2x+8}{4}[/tex], inmultim pe diagonala

[tex](x+1)*4=(2x+8)*0.5\\4x+4= x+4\\4x-x=4-4\\3x=0|:3\\x=0[/tex]

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

[tex]\frac{x}{1} *\frac{1}{3} =\frac{0,(7)}{2} *\frac{1}{3}[/tex]

[tex]\frac{x}{3} =\frac{0,(7)}{6}[/tex], inmultim pe diagonala

[tex]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}[/tex]

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

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

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

[tex]3x=19|:3\\x=\frac{19}{3}[/tex]