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