Ragazzi potreste aiutarmi nella verifica dell'equazione n,°256? Grazieeee

Sostituendo

S = [5*(-8/11) + 2]/7 - [3*(-8/11) + 1]/2 =

= (-40 + 22)/(11*7) - (-24 + 11)/(11*2) =

= -18/77 + 13/22 =

= (-36 + 91)/154 =

= 55/154 =

= (55:11)/(154:11) =

= 5/14 = D

Verifica della 265 sostituendo il risultato $\small (-7)$ all'incognita:

$\small \dfrac{1}{2}×(-7)+2-\dfrac{3+(-7)}{5} = \dfrac{1}{2}-\dfrac{5-(-7)}{10}$

$\small -\dfrac{7}{2}+2 -\dfrac{3-7}{5} = \dfrac{1}{2}-\dfrac{5+7}{10}$

$\small -\dfrac{7}{2}+2-\left(-\dfrac{4}{5}\right) = \dfrac{1}{2}-\dfrac{\cancel{12}^6}{\cancel{10}_5}$ 

$\small -\dfrac{7}{2}+2 +\dfrac{4}{5} = \dfrac{1}{2}-\dfrac{6}{5}$ 

$\small \dfrac{-35+20+8}{10} = \dfrac{5-12}{10}$

$\small -\dfrac{7}{10} = -\dfrac{7}{10}$

eguaglianza verificata.

(5x+20-2(3+x))/10 = (5-5+x)/10 

i denominatori, essendo uguali, si semplificano

(5x+20-6-2x) = x

2x = -14

x = -14/2 = -7 

(9(x-4)-x+3x)/6 = (x-9)/3

(9x-36-x+3x) = (x-9)*2

11x-36 = 2x-18

9x = 18

x = 18/9 = 2 

256)

$\small \dfrac{5x+2}{7}-\dfrac{3x+1}{2} = \dfrac{5}{14}$ $\quad \small (mcm= 14)$, quindi moltiplica tutto per 14:

$\small 2(5x+2) -7(3x+1) = 5$

$\small 10x+4 -21x-7 = 5$

$\small -11x-3 = 5$

$\small -11x = 5+3$

$\small -11x = 8$

$\small 11x = -8$

$\small \dfrac{\cancel{11}x}{\cancel{11}} = \dfrac{-8}{11}$

$\small x= -\dfrac{8}{11}$

Verifica sostituendo il risultato all'incognita:

$\small \dfrac{5×-\dfrac{8}{11}+2}{7} -\dfrac{3×-\dfrac{8}{11}+1}{2} = \dfrac{5}{14}$

$\small 2\left(5×-\dfrac{8}{11}+2\right) -7\left(3×-\dfrac{8}{11}+1\right) = 5$

$\small 2\left(-\dfrac{40}{11}+2\right) -7\left(-\dfrac{24}{11}+1\right) = 5$

$\small -\dfrac{80}{11}+4+\dfrac{168}{11}-7 = 5$

$\small \dfrac{\cancel{88}^8}{\cancel{11}_1}-3 = 5$

$\small 8-3 = 5$

$\small 5 = 5$

eguaglianza verificata.

(18x-9x+4x)/18 = 13

13x = 18*13 

x = 18*13/13 = 18 

(2(5x+2)-7(3x+1))/14 = 5/14

i denominatori, essendo uguali, si semplificano 

10x+4 -21x-7 = 5 

-11x = 8

x = -8/11

(7-3x+3(x-10))/6 = 2/6

i denominatori, essendo uguali, si semplificano 

(7-3x+3x-30) = 2

-23 = 2 ...impossibile 

(x-3-7)/7 = ((x-9)-7(x-6))/21

3(x-10)/21 = (x-9-7x+42)/21 

i denominatori, essendo uguali, si semplificano

3x-30 = -6x+33

9x = 63

x = 63/9 = 7 

(6x+8x+3x-2x)/12 = 10

15x = 120

x = 120/15 = 240/30 = 8 

(10(x+1)-4(3x-3))/20 = 20(x-3)/20

i denominatori, essendo uguali, si semplificano

10x+10-12x+12 = 20x-60

22x = 82

x = 82/22 = 41/11

(2x-9+19-2x-6x)/2 = 0

-6x+10 = 0

6x = 10

x = 10/6 = 5/3

(2(x+2)-3(x-1))/6 = 2+x-(9+x)/2

(2x+4-3x+3)/6 = (4+2x-9-x)/2

moltiplico per 6 i numeratori

-x+7 = 3(x-5)

22 = 4x

x = 22/4 = 11/2