[Risolto] Mi aiutate a risolvere espressione n. 373 il risultato è 7/2 grazie

373)

$\small \left(\dfrac{3}{20}+\dfrac{1}{5}+\dfrac{7}{15}+x\right) : x = \left(\dfrac{7}{4}+\dfrac{9}{11}·\dfrac{33}{4}-\dfrac{7}{2}\right) : \left(2+\dfrac{1}{12}\right)$

$\small \left(\dfrac{9+12+28}{60}+x\right) : x = \left(\dfrac{7}{4}+\dfrac{9}{1}·\dfrac{3}{4}-\dfrac{7}{2}\right) : \left(\dfrac{24+1}{12}\right)$

$\small \left(\dfrac{49}{60}+x\right) : x = \left(\dfrac{7}{4}+\dfrac{27}{4}-\dfrac{7}{2}\right) : \dfrac{25}{12}$

$\small \left(\dfrac{49}{60}+x\right) : x = \left(\dfrac{34}{4}-\dfrac{7}{2}\right) : \dfrac{25}{12}$

applica lo scomporre intanto a sinistra:

$\small \left(\dfrac{49}{60}+x-x\right) : x = \left(\dfrac{\cancel{34}^{17}}{\cancel4_2}-\dfrac{7}{2}\right) : \dfrac{25}{12}$

$\small \left(\dfrac{49}{60}+\cancel{x}-\cancel{x}\right) : x = \left(\dfrac{17}{2}-\dfrac{7}{2}\right) : \dfrac{25}{12}$

$\small \dfrac{49}{60} : x = \dfrac{\cancel{10}^5}{\cancel2_1} : \dfrac{25}{12}$

ora lo scomporre anche a destra:

$\small \dfrac{49}{60} : x = \left(5-\dfrac{25}{12}\right) : \dfrac{25}{12}$

$\small \dfrac{49}{60} : x = \left(\dfrac{60-25}{12}\right) : \dfrac{25}{12}$

$\small \dfrac{49}{60} : x = \dfrac{35}{12} : \dfrac{25}{12}$

$\small x = \dfrac{49}{\cancel{60}_{12}}·\dfrac{\cancel{25}^5}{12} : \dfrac{35}{12}$

$\small x = \dfrac{49}{12}·\dfrac{\cancel5^1}{\cancel{12}_1}·\dfrac{\cancel{12}^1}{\cancel{35}_7}$

$\small x = \dfrac{\cancel{49}^7}{12}·\dfrac{1}{\cancel7_1}$

$\small x = \dfrac{7}{12}$

((9+12+28)/60+x) : x = (77+297-154)/44) : 25/12

(49/60+x)*25/12 = 220x/44

49*25/720+25x/12 = 5x

1225/720 = 35x/12

x = 1225*12/(720*35)

x = 35/60 = 7/12

((54+5-9)/30-x) : x = ((66-8+15-1)/18) : ((54-40+45-9)/30)

(5/3-x) : x = 72/18*30/50

(5/3-x) : x = 4*3/5 

25/3-5x = 12x 

25/3 = 17x 

x = 25/51