Question

(8,4:x+3 5/9):4 1/6=1 1/3

Answer 1

Ответ:

Пошаговое объяснение:

(8,4 : х + 3 5/9) : 4 1/6 = 1 1/3

8,4 : х + 3 5/9 = 1 1/3 * 4 1/6 = 4/3 * 25/6

8,4 : х + 3 5/9 = 50/9

8,4 : х = 50/9 - 3 5/9 = 50/9 - 32/9 = (50-32) / 9

8,4 : х = 2

х = 8,4 : 2

х = 4,2

Answer 2

To solve the equation (8,4:x+3 5/9):4 1/6 = 1 1/3, let's break down the problem step by step.

First, let's simplify the expression on the left side of the equation:

(8,4:x+3 5/9) represents a mixed number, where the whole part is 8 and the fraction part is 4:x+3 5/9.

To simplify the fraction part, we need to convert it to a single fraction. The fraction 4:x+3 5/9 can be rewritten as:

4 + x + 3 5/9

Now, we need to convert the mixed number 3 5/9 to an improper fraction. To do that, we multiply the whole part (3) by the denominator of the fraction (9) and add the numerator (5). Then we place the sum over the denominator:

3 * 9 + 5 = 27 + 5 = 32

So, 3 5/9 is equivalent to 32/9. Substituting this into our expression, we have:

4 + x + 32/9

Next, we need to divide the entire expression by 4 1/6. Let's convert 4 1/6 to an improper fraction:

4 * 6 + 1 = 24 + 1 = 25 25/6

Now, we can rewrite the equation as:

(4 + x + 32/9) / (25/6) = 1 1/3

To simplify further, we can multiply both sides of the equation by the reciprocal of 25/6, which is 6/25. This will cancel out the division:

[(4 + x + 32/9) / (25/6)] * (6/25) = (1 1/3) * (6/25)

Simplifying the left side:

[(4 + x + 32/9) * 6] / 25 = (1 1/3) * (6/25)

Now, let's simplify the right side:

1 1/3 = (3 * 1 + 1) / 3 = 4/3

Plugging this back into the equation:

[(4 + x + 32/9) * 6] / 25 = (4/3) * (6/25)

Next, let's simplify both sides of the equation separately:

On the left side:

[(4 + x + 32/9) * 6] / 25 = (4x + 36/9 + 32/9) * 6 / 25 = [(4x + 68/9) * 6] / 25 = (24x + 408/9) / 25 = (8x + 136/3) / 25

On the right side:

(4/3) * (6/25) = 24/75 = 8/25

Now, the equation becomes:

(8x + 136/3) / 25 = 8/25

To solve for x, we can cross-multiply:

8x + 136/3 = 8

To isolate x, we subtract 136/3 from both sides:

8x = 8 - 136/3 8x = 24/3 - 136/3 8x = -112/3

Finally, divide both sides by 8 to solve for x:

x = (-112/3) / 8 x = -112/3 * 1