To solve the equation \( \frac{2}{5}(x + 15) = 26 \), we can follow these steps:
Step 1: Eliminate the fraction.
To do this, we can multiply both sides of the equation by \( 5 \) (the denominator in the fraction):
\[ 5 \cdot \frac{2}{5}(x + 15) = 5 \cdot 26 \]
This simplifies to:
\[ 2(x + 15) = 130 \]
Step 2: Distribute the 2.
Now, distribute \( 2 \) on the left side:
\[ 2x + 30 = 130 \]
Step 3: Isolate the term containing \( x \).
Next, we want to isolate \( 2x \) by subtracting \( 30 \) from both sides:
\[ 2x + 30 - 30 = 130 - 30 \]
This simplifies to:
\[ 2x = 100 \]
Step 4: Solve for \( x \).
Finally, divide both sides by \( 2 \):
\[ x = \frac{100}{2} \]
This gives us:
\[ x = 50 \]
Conclusion:
The value of \( x \) is \( \boxed{50} \).