To solve the equation \( \frac{2}{5}(x+15) = 26 \), we will follow these steps:
Step 1: Eliminate the fraction
To eliminate the fraction, we can multiply both sides of the equation by 5:
\[ 5 \cdot \frac{2}{5}(x + 15) = 5 \cdot 26 \]
This simplifies to:
\[ 2(x + 15) = 130 \]
Step 2: Distribute the 2
Next, we will distribute the 2 on the left side:
\[ 2x + 30 = 130 \]
Step 3: Isolate the term with x
To isolate the \( 2x \) term, subtract 30 from both sides:
\[ 2x = 130 - 30 \]
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 gives:
\[ x = 50 \]
Conclusion
Thus, the value of \( x \) is \( \boxed{50} \).