Question

dau coroana! cu tot cu rezolvare!!corect! si va rog sa nu mai iesiti

Answer 1

a) $\frac{x}{6}= \frac{2}{3}$
3x=12
x=4

b) $\frac{12}{x}= \frac{4}{5}$
$\frac{12}{x}= \frac{4}{5} ; x \neq 0$
60=4x
4x=60
x=15; x≠0
x=15

c) $\frac{10}{5}= \frac{x}{12}$
$2= \frac{x}{12}$
24=x
x=24

d) $\frac{6}{7}= \frac{12}{x}$
$\frac{6}{7}= \frac{12}{x}; x \neq 0$
6x=84
x=14; x≠0
x=14

e) $\frac{x}{5}= \frac{1}{1}$
$\frac{x}{5}=1$
x=5

f) $\frac{x}{4}=2 \frac{1}{2}$
$\frac{x}{4}= 1$
x=4

g) $\frac{1}{x}= 0.2$
$\frac{1}{x}= 0.2; x \neq 0$
1=0.2x
0.2x=1
x=5; x≠0
x=5

h) $\frac{x}{0.6}= 1$
$\frac{x}{ \frac{3}{5} } =1$
$\frac{5x}{3} =1$
5x=3
$x= \frac{3}{5}$ sau x=0.6

i) $\frac{1 } { \frac{2} {x} } + \frac{2}{3}$
$\frac{7}{ \frac{6}{x} }$
$\frac{7}{6x}$

j) $\frac{x}{ 4\frac{1}{2}-1 \frac{3}{4} }$
$\frac{x}{ 2-\frac{3}{4} }$
$\frac{x}{ \frac{5}{4} }$
$\frac{4x}{5}$

k) $\frac{2x}{3}= \frac{6}{12}$
$\frac{2x}{3}= \frac{1}{2}$
4x=3
$x= \frac{3}{4}$ sau x=0.75

l) $\frac{5}{6x} =1 \frac{1}{24}$
$\frac{5}{6x} =1 \frac{1}{24}; x \neq 0$
$\frac{5}{6x} =\frac{1}{24}$
120=6x
6x=120
x=20; x≠0
x=20

m) $\frac{x+2}{3}= \frac{4}{5}$
5(x+2)=12
5x+10=12
5x=12-10
5x=2
$x= \frac{2}{5}$ sau x=0.4

n) $2+ \frac{1}{ \frac{3}{7- \frac{2}{3} } }$
$2+ \frac{1}{ \frac{3}{ \frac{19}{3} } }$
$\frac{19}{2+ \frac{3}{3} }$
$2+ \frac{19}{9}$
$\frac{37}{9}$ sau $4 \frac{1}{9}$  ≈ 4.11111

o) $\frac{1}{x+1}= \frac{2}{x+2}$
$\frac{1}{x+1}= \frac{2}{x+2} ; x \neq -1; x \neq -2$
x+2=2(x+1)
x+2=2x+2
x=2x
x-2x=0
-x=0
x=0; x≠-1; x≠-2
x=0

p) $\frac{x-3}{2} = \frac{1}{ \frac{2}{1+ \frac{1}{4} } }$
$\frac{x-3}{2}= \frac{1}{ \frac{2}{ \frac{5}{4} } }$
$\frac{x-3}{2}= \frac{5}{ \frac{4}{2} }$
$\frac{x-3}{2} = \frac{5}{8}$
8(x-3)=10
8x-24=10
8x=10+24
8x=34
$x= \frac{17}{4}$ sau $x=4 \frac{1}{4}$ sau x=4.25