To solve the equation \( \frac{2}{5}(x + 15) = 26 \), we will follow the steps outlined below:
Step 1: Eliminate the Fraction
To eliminate the fraction \(\frac{2}{5}\), multiply both sides of the equation by \(5\):
\[ 5 \cdot \left( \frac{2}{5}(x + 15) \right) = 5 \cdot 26 \]
This simplifies to:
\[ 2(x + 15) = 130 \]
Step 2: Distribute the 2
Next, distribute \(2\) on the left side:
\[ 2x + 30 = 130 \]
Step 3: Isolate the Variable Term
Now, we will isolate the term containing \(x\) by subtracting \(30\) from both sides:
\[ 2x + 30 - 30 = 130 - 30 \]
This simplifies to:
\[ 2x = 100 \]
Step 4: Solve for \(x\)
Now, divide both sides by \(2\) to solve for \(x\):
\[ x = \frac{100}{2} \]
This simplifies to:
\[ x = 50 \]
Conclusion
The value of \(x\) is
\[ \boxed{50} \]