Question

4 5/36 - (1 4/9 - x) = 1 17/18

Answer 1

Пошаговое объяснение:

Все решения на фото) Если не сложно, отметь мое решение лучшим

Answer 2

To solve the equation 4 5/36 - (1 4/9 - x) = 1 17/18, we'll simplify each side step by step.

Let's start by converting all mixed numbers into improper fractions:

4 5/36 = (4 * 36 + 5) / 36 = 149/36 1 4/9 = (1 * 9 + 4) / 9 = 13/9 1 17/18 = (1 * 18 + 17) / 18 = 35/18

Now we can substitute these values back into the equation:

149/36 - (13/9 - x) = 35/18

Next, let's simplify the expression (13/9 - x) by finding a common denominator:

13/9 - x = 13/9 - (x * 9/9) = 13/9 - 9x/9 = (13 - 9x) / 9

Substituting this back into the equation:

149/36 - (13 - 9x) / 9 = 35/18

Now we need to find a common denominator for 36 and 9, which is 36:

(149/36) * (4/4) - (13 - 9x) / 9 = 35/18

596/144 - (13 - 9x) / 9 = 35/18

Now we can combine the fractions:

(596/144) - ((13 - 9x) / 9) = 35/18

To eliminate the fraction in the equation, we can multiply through by the common denominator, which is 144 * 9 = 1296:

1296 * (596/144) - 1296 * ((13 - 9x) / 9) = 1296 * (35/18)

Cancelling out the denominators:

1296 * (596/144) - 144 * (13 - 9x) = 72 * 35

Simplifying the left side:

1296 * (149/36) - 144 * (13 - 9x) = 2520

Multiplying and simplifying:

(1296 * 149)/36 - 144 * 13 + 144 * 9x = 2520

Now we can solve for x. Let's continue solving this equation step by step:

(1296 * 149)/36 - 1872 + 1296 * 9x = 2520

Multiplying and simplifying:

(192304/36) + 1296 * 9x = 2520 + 1872

Simplifying further:

5347 + 1296 * 9x = 4392

Rearranging the equation:

1296 * 9x = 4392 - 5347

1296 * 9x = -952

Dividing by 1296 * 9:

9x = -952 / (1296 * 9)

9x = -952 / 11664

x = -952 / 11664

x ≈ -0.0817 (rounded to four decimal places)

Therefore, the approximate solution for x is -0.0817.