Question

3 2/3:(x-2 4/15)=3 5/13 решить уравнение

Answer 1

Пошаговое объяснение:

$\displaystyle 3\frac{2}{3} : ( x- 2 \frac{4}{15})= 3 \frac{5}{13}\\ \\ x- 2 \frac{4}{15}= 3\frac{2}{3} : 3 \frac{5}{13} \\ \\ x- 2 \frac{4}{15}= \frac{11}{3} : \frac{44}{13}\\ \\ x- 2 \frac{4}{15}= \frac{11}{3} * \frac{13}{44}\\ \\ x- 2 \frac{4}{15}= \frac{13}{12}\\ \\ x= \frac{13}{12} + 2 \frac{4}{15}= 1 \frac{1}{12} + 2 \frac{4}{15}= 1 \frac{5}{60} + 2 \frac{16}{60}= 3 \frac{21}{60}= 3 \frac{7}{20}$

Answer 2

Ответ:

$\tt \displaystyle 3\frac{7}{20}$

Пошаговое объяснение:

$\tt \displaystyle 3\frac{2}{3} :(x-2\frac{4}{15} )=3\frac{5}{13}$

$\tt \displaystyle 3\frac{2}{3} =3\frac{5}{13} \cdot (x-2\frac{4}{15} )$

$\tt \displaystyle x-2\frac{4}{15} =3\frac{2}{3} : 3\frac{5}{13}$

$\tt \displaystyle x-2\frac{4}{15} =\frac{11}{3} : \frac{44}{13}$

$\tt \displaystyle x =\frac{11}{3} \cdot \frac{13}{44}+2\frac{4}{15}=\frac{1}{3} \cdot \frac{13}{4}+2\frac{4}{15}=\frac{13}{12}+2\frac{4}{15}=1\frac{1}{12}+2\frac{4}{15}=\\\\=1\frac{1 \cdot 5}{12 \cdot 5}+2\frac{4 \cdot 4}{15 \cdot 4}=1\frac{5}{60}+2\frac{16}{60}=3\frac{5+16}{60}=3\frac{21}{60}=3\frac{21:3}{60:3}=3\frac{7}{20}.$

Проверка:

$\tt \displaystyle 3\frac{2}{3} :(3\frac{7}{20}-2\frac{4}{15} )=\frac{11}{3} :(3\frac{7 \cdot 3}{20 \cdot 3}-2\frac{4 \cdot 4}{15 \cdot 4} )=\frac{11}{3} :(3\frac{21}{60}-2\frac{16}{60} )=\\\\=\frac{11}{3} :(1\frac{21-16}{60})=\frac{11}{3} :(1\frac{5}{60})=\frac{11}{3} :(1\frac{5:5}{60:5})=\frac{11}{3} :(1\frac{1}{12})=\frac{11}{3} :\frac{13}{12}=\\\\=\frac{11}{3} \cdot \frac{12}{13}=\frac{11 \cdot 12}{3 \cdot 13}=\frac{11 \cdot 4 \cdot 3}{3 \cdot 13}=\frac{11 \cdot 4}{13}=\frac{44}{13}=3\frac{5}{13}$

Верно!

Answer 3

To solve the equation, we'll start by simplifying the left side of the equation by multiplying both sides by the reciprocal of the fraction on the left side:

3 2/3:(x-2 4/15)=3 5/13

13/3 * (3 2/3):(x-2 4/15) = 13/3 * 3 5/13

13(11/3) * (x-2 4/15) = 52/3

Now we'll simplify the right side of the equation:

13(11/3) * (x-2 4/15) = 52/3

143/3 * (x-74/15) = 52/3

Multiplying both sides by the reciprocal of 143/3:

(x-74/15) = 52/3 * 3/143

(x-74/15) = 4/11

Adding 74/15 to both sides:

x = 4/11 + 74/15

Now we'll find a common denominator and add the fractions:

x = (60/11 + 74/11 * 3/3)/15

x = (60/11 + 222/11)/15

x = 282/11 * 1/15

x = 282/165

Therefore, the solution to the equation is x = 282/165.