Question

4 5/7 * (x + 0, 28) = 1 4/7

Answer 1

Ответ:

x = 4/75

Пошаговое объяснение:

4 5/7 * (x + 0,28) = 1 4/7

Сначала умножим 4 5/7 на скобку

4 5/7 * (x + 0,28) = 4 5/7x + 4 5/7 * 0,28 = 4 5/7x + 33/7 * 28/100 = 4 5/7x + 1 8/25

Получили выражение

4 5/7x + 1 8/25 = 1 4/7

Теперь перенесём 1 8/25 в левую часть

4 5/7x = 1 4/7 - 1 8/25

4 5/7x = 4/7 - 8/25

4 5/7x = 100/175 - 56/175

4 5/7x = 44/175

x = 44/175 : 4 5/7

x = 44/175 : 33/7

x = 44/175 * 7/33

x = 4/75

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Answer 2

To solve the equation 4 5/7 * (x + 0.28) = 1 4/7, you'll want to follow these steps:

Step 1: Convert the mixed numbers to improper fractions. 4 5/7 can be written as (74 + 5)/7 = 33/7. 1 4/7 can be written as (71 + 4)/7 = 11/7.

Now the equation becomes:

(33/7) * (x + 0.28) = 11/7

Step 2: Cancel out the common factors on both sides of the equation. In this case, you can see that 7 is a common factor on both sides, so you can divide both sides by 7 to simplify the equation:

(33/7) * (x + 0.28) / 7 = (11/7) / 7

Now, the equation simplifies to:

(33/7) * (x + 0.28) = 11/49

Step 3: Multiply both sides of the equation by the reciprocal of (33/7) to isolate x.

(x + 0.28) = (11/49) / (33/7)

Reciprocal of (33/7) is (7/33).

x + 0.28 = (11/49) * (7/33)

Now, calculate the right side:

x + 0.28 = (77/1617)

Step 4: Subtract 0.28 from both sides to solve for x:

x = (77/1617) - 0.28

Now, you can simplify further:

x = (77/1617) - (280/1000)

To add or subtract fractions, you need a common denominator. In this case, the common denominator is 1617 * 1000 = 1617000.

x = (771000 - 2801617) / 1617000

Now, perform the calculations:

x = (77000 - 453160) / 1617000 x = -376160 / 1617000

Now, you can simplify this fraction further by finding the greatest common divisor (GCD) of the numerator and denominator and dividing both by it:

GCD of 376160 and 1617000 = 40

x = (-9404 / 40425)

So, the solution to the equation is:

x ≈ -0.2329 (rounded to four decimal places)