(1,1/2÷х+2,2/5)×1,2/3-1,2/3=2,5/6

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Let's solve the equation step by step.

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

(1,1/2 ÷ x + 2,2/5) × 1,2/3 - 1,2/3

To simplify the division, we can convert the mixed number 1,1/2 to an improper fraction:

1,1/2 = 3/2

So, the equation becomes:

(3/2 ÷ x + 2,2/5) × 1,2/3 - 1,2/3

Now, we can simplify the multiplication:

[(3/2 ÷ x) + 2/5] × 4/3

To perform the multiplication, we need to find a common denominator for the fractions:

[(3/2x) + (2/5)] × 4/3

Next, we can simplify further:

(12/6x + 8/5) × 4/3

Now, let's find a common denominator for the fractions:

[(24/6x) + (24/5)] × 4/3

Combining the fractions:

(24/6x + 24/5) × 4/3

Now, we need to multiply the numerators and denominators:

(96/6x + 96/5) × 4/3

Let's add the two fractions:

(96/6x + 576/30x) × 4/3

We can combine the fractions by finding a common denominator:

(96/6x + 576/30x) × 4/3

Simplifying further:

(16/6x + 96/30x) × 4/3

Combining the fractions:

(48/6x + 96/30x) × 4/3

Next, we can simplify:

(8/x + 16/5x) × 4/3

To combine the fractions, we need a common denominator:

(40/5x + 16/5x) × 4/3

Now, we can simplify the fractions by adding them:

(56/5x) × 4/3

Multiplying the fractions:

224/15x

So, the simplified left side of the equation is 224/15x.

Now, we can rewrite the equation:

224/15x = 2,5/6

Finally, we can solve for x:

224/15x = 17/6

x = (224/15) ÷ (17/6)
x = (224/15) × (6/17)
x = 1344/255
x = 64/17

Therefore, the value of x is 64/17.