N° 937

(5 - 1/3 * 3/2 + x) ÷ x = (5/2 + 1/3 + 3/2  * 4/3) ÷ (5 + 1/3 - 3/2 * 4/3);

proporzione.

primo membro:

(5 - 1/3 * 3/2 + x) ÷ x;

(5 - 1/2 + x) : x = 

= (10/2 - 1/2 + x) : x

= (9/2 + x) : x.

secondo membro dopo l'uguale:

(5/2 + 1/3 + 3/2  * 4 /3) ÷ (5 + 1/3 - 3/2 * 4/3);

(5/2 + 1/3 + 2/1) ÷ (5 + 1/3 - 2/1) =

(15/6 + 2/6 + 12/6) : (15/3 + 1/3 - 6/3) =

(29/6) : (10/3);

(9/2 + x) : x = (29/6) : (10/3);

proporzione:  (proprietà dello scomporre);

(9/2 + x - x) : x = (29/6 - 10/3) : 10/3

(9/2) : x = (29/6 - 20/6) : 10/3;

(9/2) : x = (9/6) : 10/3;

(9/2) : x = (3/2) : 10/3;

x = (9/2) * (10/3) : (3/2);

x = (9/2) * (10/3) * (2/3);

x = (9 * 10 * 2) / (2 * 3 * 3);

x = 10.

Ciao.

(5-1/3x3/2+x)÷x=(5/2+1/3+3/2x4/3)÷(5+1/3-3/2x4/3)

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$\small \left(5-\dfrac{1}{3}·\dfrac{3}{2}+x\right) ÷ x = \left(\dfrac{5}{2}+\dfrac{1}{3}+\dfrac{3}{2}·\dfrac{4}{3}\right) ÷ \left(5+\dfrac{1}{3}-\dfrac{3}{2}·\dfrac{4}{3}\right) $

$\small \left(5-\dfrac{1}{\cancel3_1}·\dfrac{\cancel3^1}{2}+x\right) ÷ x = \left(\dfrac{5}{2}+\dfrac{1}{3}+\dfrac{\cancel3^1}{\cancel2_1}·\dfrac{\cancel4^2}{\cancel3_1}\right) ÷ \left(5+\dfrac{1}{3}-\dfrac{\cancel3^1}{\cancel2_1}·\dfrac{\cancel4^2}{\cancel3_1}\right) $

$\small \left(5-\dfrac{1}{2}+x\right) ÷ x = \left(\dfrac{5}{2}+\dfrac{1}{3}+2\right) ÷ \left(5+\dfrac{1}{3}-2\right) $

$\small \left(\dfrac{10-1}{2}+x\right) ÷ x = \left(\dfrac{15+2+12}{6}\right) ÷ \left(\dfrac{15+1-6}{3}\right) $

$\small \left(\dfrac{9}{2}+x\right) ÷ x = \dfrac{29}{6} ÷ \dfrac{10}{3} $

$\small\text{applica lo scomporre:}$

$\small \left(\dfrac{9}{2}+x-x\right) ÷ x = \left(\dfrac{29}{6}-\dfrac{10}{3}\right) ÷ \dfrac{10}{3} $

$\small \left(\dfrac{9}{2}\cancel{+x}\cancel{-x}\right) ÷ x = \left(\dfrac{29-20}{6}-\right) ÷ \dfrac{10}{3} $

$\small \dfrac{9}{2} ÷ x = \dfrac{\cancel9^3}{\cancel6_2} ÷ \dfrac{10}{3} $

$\small \dfrac{9}{2} ÷ x = \dfrac{3}{2} ÷ \dfrac{10}{3} $

$\small x= \dfrac{\dfrac{\cancel9^3}{\cancel2_1}·\dfrac{\cancel{10}^5}{\cancel3_1}}{\dfrac{3}{2}} $

$\small x= \cancel3^1·5·\dfrac{2}{\cancel3_1} $

$\small x= 5·2 $

$\small x= 10 $