Question

Aflati x astfel incat fiecare fractie sa fie echivalenta cu 4/9:a) x/18 b)12/x c)x+1/27 d)5x+1/36 e)2x/81 f) 36/11x-7 g)3x+2/11x-4

Answer 1

 $a) \frac{x}{18}= \frac{4}{9}$
⇒x=(18×4):9=8;  x=8

$b) \frac{12}{x}= \frac{4}{9}$
⇒x=12×9:4=27,
x=27
 c)
$\frac{x+1}{27}= \frac{4}{9} \\ \\ 9x+9=4*27 \\ \\ 9x=108-9 \\ \\ x=99:9 \\ \\ x=1$
d)
$\frac{5x+1}{36}= \frac{4}{9} \\ \\ 45x+9=4*36 \\ \\ 45x=144-9 \\ \\ 45x=135 \\ \\ x=3$

e)
$\frac{2x}{81}= \frac{4}{9} \\ \\ x= \frac{81*4}{9*2} \\ \\ x=18$

 f)
$\frac{36}{11x-7}= \frac{4}{9} \\ \\ 36*9=4*(11x-7) \\ \\ 324=44x-28 \\ \\ 324+28=44x \\ \\ 352=44x \\ \\ x=352:44 \\ \\ x=8$

g)
$\frac{3x+2}{11x-4} = \frac{4}{9} \\ \\ 9(3x+2)=4(11x-4) \\ \\ 27x+18=44x-16 \\ \\ 34=17x \\ \\ x=34:17 \\ \\ x=2$