Question

Determina x din egalitatile!:
a) x+1/5 = 4/2
b)3/5 = 7x-2/20
c)5x-2/2x+3 = 8/7

Answer 1

a )

x + 1 / 5 = 4 / 2 = 2

x = 2 - 1 / 5

x = ( 10 - 1 ) / 5

x = 9 / 5

Daca egalitatea e de forma ( x + 1 ) / 5 = 2 , atunci solutia va fi :

x + 1 = 10

x = 10 - 1

x = 9

_____________

b)

3 / 5 = 7 x - 2 / 20

7 x - 1 / 10 = 3 / 5

7 x = 3 / 5 + 1 / 10 = ( 6 + 1 ) / 10 = 7 / 10

x = 7 / 10 : 7 = 7 / 10 x 1 / 7

x = 1 / 10

____________

Daca egalitatea e de forma ( 7 x - 2 ) / 20 = 3 / 5, atunci solutia va fi:

5 ( 7 x - 2 ) = 3 x 20

35 x - 10 = 60

35 x = 70

x = 70 / 35

x = 2

________________

c )

( 5 x - 2 ) / ( 2 x + 3 ) = 8 / 7

7 ( 5 x - 2 ) = 8 ( 2 x + 3 )

35 x - 14 = 16 x + 24

35 x - 16 x = 24 + 14

19 x = 38

x = 38 / 19

x = 2

________________

Answer 2

$a)x + \frac{1}{5} = \frac{4}{2} \\ \\ x + \frac{1}{5} = 2 \\ \\ x = 2 - \frac{1}{5} = \frac{9}{5} \\ \\ b) \frac{3}{5} = 7x - \frac{2}{20} \\ \\ \frac{3}{5} = 7x - \frac{1}{10} \\ \\ \frac{3}{5} + \frac{1}{10} = 7x \\ \\ \frac{7}{10} = x \\ \\ \frac{ \frac{7}{10} }{7} = x \\ \\ \frac{1}{10} = x \\ \\ x = \frac{1}{10} \\ \\ c) \frac{5x - 2}{2x + 3} = \frac{8}{7} \\ \\ 5x - 2 = \frac{8}{7}(2x + 3) \\ \\ 5x - 2 = \frac{8(2x + 3)}{7} \\ \\ 35x - 14 = 8(2x + 3) \\ \\ 35x - 14 = 16x + 24 \\ \\ 35 = 16x + 24 + 14 \\ \\ 35x = 16x + 38 \\ \\ 35x - 16x = 38 \\ \\ 19x = 38 \\ \\ x = \frac{38}{19} = 2$