Solve using the addition principle. Don't forget to perform a check. \( x+\frac{1}{11}=\frac{7}{11} \)

To solve the equation \( x + \frac{1}{11} = \frac{7}{11} \), we can use the addition principle. We want to isolate \( x \), so we need to subtract \( \frac{1}{11} \) from both sides of the equation. Starting with the original equation: \( x + \frac{1}{11} = \frac{7}{11} \) Subtract \( \frac{1}{11} \) from both sides: \( x = \frac{7}{11} - \frac{1}{11} \) Now, since they have the same denominator, we can simply subtract the numerators: \( x = \frac{7 - 1}{11} = \frac{6}{11} \) Now, let's perform a check by substituting \( x \) back into the original equation: \( \frac{6}{11} + \frac{1}{11} = \frac{7}{11} \) This simplifies to \( \frac{7}{11} = \frac{7}{11} \), confirming our solution is correct. So, the solution to the equation is: \( x = \frac{6}{11} \)