To solve the equation \(\frac{1}{5}(x + 15) = 26\), we can follow these steps:
Step 1: Eliminate the Fraction
To eliminate the fraction, multiply both sides of the equation by 5:
\[ 5 \cdot \frac{1}{5}(x + 15) = 5 \cdot 26 \]
This simplifies to:
\[ x + 15 = 130 \]
Step 2: Isolate x
Next, we need to isolate \(x\) by subtracting 15 from both sides:
\[ x + 15 - 15 = 130 - 15 \]
Simplifying this gives:
\[ x = 115 \]
Step 3: Verify the Solution
To ensure our solution is correct, we can substitute \(x = 115\) back into the original equation:
\[ \frac{1}{5}(115 + 15) = 26 \]
Calculating inside the parentheses:
\[ 115 + 15 = 130 \]
Now substituting:
\[ \frac{1}{5}(130) = 26 \]
Calculating the left side:
\[ \frac{130}{5} = 26 \]
Since both sides of the equation are equal, our solution is verified.
Final Answer
Thus, the value of \(x\) is:
\[ \boxed{115} \]