2/3(8*187/481-6(5/11*187/481-5)+1,3)+10(0,14*187/481+0,5)-2*187/481=27

To verify the equation \( \frac{2}{3}\left(8 \cdot \frac{187}{481} - 6\left(\frac{5}{11} \cdot \frac{187}{481} - 5\right) + 1.3\right) + 10\left(0.14 \cdot \frac{187}{481} + 0.5\right) - 2 \cdot \frac{187}{481} = 27 \), we will simplify each term step by step.

1. Calculate \( \frac{187}{481} \): First, compute \( \frac{187}{481} \approx 0.388 \) (exact computation can be made, but for brevity, we can use this approximation).

2. Calculate \( 8 \cdot \frac{187}{481} \): \[ 8 \cdot \frac{187}{481} \approx 8 \cdot 0.388 = 3.104 \]

3. Calculate \( \frac{5}{11} \cdot \frac{187}{481} \): \[ \frac{5}{11} \cdot \frac{187}{481} \approx 0.4545 \cdot 0.388 \approx 0.176 \] So this gives us: \[ 6\left(\frac{5}{11} \cdot \frac{187}{481} - 5\right) = 6(0.176 - 5) \approx 6(-4.824) \approx -28.944 \]

4. Combine the terms inside the first parentheses: \[ 8 \cdot \frac{187}{481} - 6\left(\frac{5}{11} \cdot \frac{187}{481} - 5\right) + 1.3 \approx 3.104 - (-28.944) + 1.3 \approx 33.348 \] Then, simplifying: \[ \frac{2}{3} \cdot 33.348 \approx 22.232 \]

5. Calculate the second term \( 10\left(0.14 \cdot \frac{187}{481} + 0.5\right) \): \[ 0.14 \cdot \frac{187}{481} \approx 0.054 \quad \Rightarrow \quad 10(0.054 + 0.5) = 10(0.554) = 5.54 \]

6. Calculate the term \( -2 \cdot \frac{187}{481} \): \[ -2 \cdot \frac{187}{481} \approx -0.776 \]

7. Combine everything: Combine the computed results: \[ 22.232 + 5.54 - 0.776 \approx 27 \]

So the entire expression simplifies correctly to 27, confirming the equality:

\[ \frac{2}{3}(8 \cdot \frac{187}{481} - 6(\frac{5}{11} \cdot \frac{187}{481} - 5) + 1.3) + 10(0.14 \cdot \frac{187}{481} + 0.5) - 2 \cdot \frac{187}{481} = 27 \]

Thus, the equation is verified.