Question

10. Решите уравнения: даю 60баллов​

Answer 1

Ответ:

Решить уравнения .  

Применяем правило нахождения неизвестного делителя : чтобы найти неизвестный делитель, надо делимое разделить на частное .

$\bf \displaystyle 1)\ \ 4\frac{4}{5}:(3x-2,5)=\frac{4}{17}\\\\(3x-2,5)=4\frac{4}{5}:\frac{4}{17}\ \ \ \to \ \ \ 3x-2,5=\frac{24}{5}\cdot \frac{17}{4}\ \ ,\ \ \ \ 3x-2,5=\frac{6\cdot 17}{5}\ ,\\\\3x=\frac{102}{5}+\frac{5}{2}\ \ \ ,\ \ \ 3x=\frac{229}{10}\ \ ,\ \ \ x=\frac{229}{10}:3\ \ ,\ \ \ x=\frac{229}{30} \ \ ,\ \ x=7\frac{19}{30}$  

$\bf \displaystyle 2)\ \ \frac{28}{29}:\Big(2,5x+1\frac{3}{4}\Big)=\frac{4}{29}\\\\\\2,5x+\frac{7}{4}=\frac{28}{29}:\frac{4}{29}\ \ \ \to \ \ \ 2,5x+\frac{7}{4}=\frac{28}{29}\cdot \frac{29}{4}\ \ ,\ \ \ 2,5x+\frac{7}{4}=7\ \ ,\\\\\\2,5x=7-\frac{7}{4}\ \ ,\ \ 2,5x=\frac{21}{4}\ \ ,\ \ \ x=\frac{21}{4}:\frac{5}{2}\ \ ,\ \ \ x=\frac{21}{4}\cdot \frac{2}{5}\ \ ,\\\\\\x=\frac{21}{10}\ \ ,\ \ \ x=2\frac{1}{10}\ \ ,\ \ x=2,1$  

$\bf \displaystyle 3)\ \ 11\frac{1}{3}:\Big(\Big(\frac{1}{2}\, x-2\frac{1}{3}\Big)-1\frac{1}{2}\Big)=\frac{4}{21}\\\\\\\frac{34}{3}:\Big(\Big(\frac{1}{2}\, x-\frac{7}{3}\Big)-\frac{3}{2}\Big)=\frac{4}{21}\ \ ,\ \ \ \ \Big(\Big(\frac{1}{2}\, x-\frac{7}{3}\Big)-\frac{3}{2}\Big)=\frac{34}{3}:\frac{4}{21}\ \ ,\\\\\\\Big(\frac{1}{2}\, x-\frac{7}{3}\Big)=\frac{34}{3}\cdot \frac{21}{4}+\frac{3}{2}\ \ ,\ \ \ \frac{1}{2}\, x-\frac{7}{3}=\frac{17}{1}\cdot \frac{7}{2}+\frac{3}{2}\ \ ,$    

$\bf \displaystyle \frac{1}{2}\, x-\frac{7}{3}=\frac{119}{2}+\frac{3}{2}\ \ \ ,\ \ \ \frac{1}{2}\, x-\frac{7}{3}=\frac{122}{2}\ \ ,\ \ \ \frac{1}{2}\, x-\frac{7}{3}=61\ \ ,\\\\\\\frac{1}{2}\, x=\frac{7}{3}+61\ \ ,\ \ \ \frac{1}{2}\, x=\frac{190}{3}\ \ \ ,\ \ \ x=\frac{190\cdot 2}{3}\ \ ,\ \ \ x=\frac{380}{3}\ \ ,\ \ x=126\frac{2}{3}$  

$\bf \displaystyle 4)\ \ \frac{1}{4}:\Big(1\dfrac{5}{9}-\Big(\frac{3}{8}\, x-3\frac{1}{2}\Big)\Big)=3\\\\\\\frac{1}{4}:\Big(\dfrac{14}{9}-\Big(\frac{3}{8}\, x-\frac{7}{2}\Big)\Big)=3\ \ \ ,\ \ \ \frac{14}{9}-\Big(\frac{3}{8}\, x-\frac{7}{2}\Big)=\frac{1}{4}:3\ \ \ ,\\\\\\\Big(\frac{3}{8}\, x-\frac{7}{2}\Big)=\frac{14}{9}-\frac{1}{12}\ \ ,\ \ \ \frac{3}{8}\, x-\frac{7}{2}=\frac{14\cdot 4-3}{36}\ \ ,$  

$\bf \displaystyle \frac{3}{8}\, x-\frac{7}{2}=\frac{53}{36}\ \ \ ,\ \ \ \frac{3}{8}\, x=\frac{53}{36}+\frac{7}{2} \ ,\ \ \ \frac{3}{8}\, x=\frac{179}{36}\ \ ,\ \ x=\frac{179\cdot 8}{36\cdot 3}\ \ ,\\\\\\x=\frac{179\cdot 2}{9\cdot 3} \ \ ,\ \ \ x=\frac{358}{27}\ \ \ ,\ \ \ x=13\frac{7}{27}$      

Answer 2

Пошаговое объяснение:

№1

4 4/5 : (3х - 2,5) = 4/17

3х - 2,5 = 4 4/5 : 4/17

3х - 2,5 = 24/5 * 17/4

3х - 2,5 = 6/5 * 17/1

3х - 2,5 = 102/5

3х = 102/5 + 2,5

3х = 204/10 + 25/10

3х = 229/10

х = 229/10 : 3

х = 229/10 * 1/3

х = 229/30

х = 7 19/30

№2

28/29 : (2,5х + 1 3/4) = 4/29

2,5х + 1 3/4 = 28/29 : 4/29

2,5х + 1,75 = 28/29 * 29/4

2,5х + 1,75 = 7/1 * 1/1

2,5х + 1,75 = 7

2,5х = 7 - 1,75

2,5х = 5,25

х = 5,25 : 2,5

х = 2,1

№3

11 1/3 : ((1/2х - 2 1/3) - 1 1/2) = 4/21

(1/2х - 2 1/3) - 1 1/2 = 11 1/3 : 4/21

(1/2х - 2 1/3) - 1 1/2 = 34/3 * 21/4

(1/2х - 2 1/3) - 1 1/2 = 17/1 * 7/2

(1/2х - 2 1/3) - 1 1/2 = 119/2

1/2х - 2 1/3 = 119/2 + 1 1/2

1/2х - 2 1/3 = 122/2

1/2х - 2 1/3 = 61

1/2х = 61 + 2 1/3

1/2х = 63 1/3

х = 63 1/3 : 1/2

х = 190/3 * 2/1

х = 380/3

х = 126 2/3

№4

1/4 : (1 5/9 - (3/8х - 3 1/2)) = 3

1 5/9 - (3/8х - 3 1/2) = 1/4 : 3

1 5/9 - (3/8х - 3 1/2) = 1/4 * 1/3

1 5/9 - (3/8х - 3 1/2) = 1/12

3/8х - 3 1/2 = 1 5/9 - 1/12

3/8х - 3 1/2 = 1 20/36 - 3/36

3/8х - 3 1/2 = 1 17/36

3/8х = 1 17/36 + 3 1/2

3/8х = 1 17/36 + 3 18/36

3/8х = 4 35/36

х = 4 35/36 : 3/8

х = 179/36 * 8/3

х = 179/9 * 2/3

х = 358/27

х = 13 7/27