Question

2 2/3:(x+1/3)=1 1/2:(x-1 1/8) Ответ:3 Нужно решение

Answer 1

Свойство пропорции: произведение крайних членов равно произведению средних, решаем:

$\cfrac{2 \frac{2}{3} }{x+ \frac{1}{3} } = \cfrac{1 \frac{1}{2} }{x- 1\frac{1}{8} } \\ \\ x \neq - \frac{1}{3}; \ \ x \neq 1 \frac{1}{8} \\\\ 2 \frac{2}{3}(x-1 \frac{1}{8} )=1 \frac{1}{2} (x+ \frac{1}{3} ) \\ \\ \frac{8}{3}(x- \frac{9}{8} )= \frac{3}{2} (x+ \frac{1}{3} ) \\ \\ \frac{8}{3}x- 3= \frac{3}{2} x+ \frac{1}{2} \\\\\frac{8}{3}x-\frac{3}{2} x= \frac{1}{2}+3 \\ \\ \frac{7}{6}x= \frac{7}{2} \\ \\ x= \frac{7}{2}: \frac{7}{6}= \frac{7}{2}: \frac{6}{7}=3$

Answer 2

To solve the equation, let's first convert the mixed numbers into improper fractions:

2 2/3 = (3 * 2 + 2) / 3 = 8/3 1 1/2 = (2 * 1 + 1) / 2 = 3/2 1 1/8 = (8 * 1 + 1) / 8 = 9/8

Now the equation becomes:

(8/3) / (x + 1/3) = (3/2) / (x - 9/8)

To eliminate the denominators, we can multiply both sides of the equation by the least common multiple (LCM) of 3 and 8, which is 24:

24 * (8/3) / (x + 1/3) = 24 * (3/2) / (x - 9/8)

Simplifying further:

(8 * 8) / (x + 1/3) = (3 * 12) / (x - 9/8)

64 / (x + 1/3) = 36 / (x - 9/8)

Now, cross-multiply:

64 * (x - 9/8) = 36 * (x + 1/3)

Expand the products:

64x - 64(9/8) = 36x + 36(1/3)

Simplify:

64x - 72 = 36x + 12

Now, isolate the variable terms on one side and constants on the other side:

64x - 36x = 12 + 72

28x = 84

Finally, solve for x:

x = 84 / 28

x = 3

Therefore, the solution to the equation is x = 3.