To determine the value of \( x \) in the equation
\[ \frac{2}{5}(x + 15) = 26, \]
we can 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 distribute the 2 on the left side of the equation:
\[ 2x + 30 = 130. \]
Step 3: Isolate the Term with x
Now, we need to isolate the term with \( x \). We can do this by subtracting 30 from both sides of the equation:
\[ 2x + 30 - 30 = 130 - 30. \]
This simplifies to:
\[ 2x = 100. \]
Step 4: Solve for x
Finally, we divide both sides of the equation by 2 to solve for \( x \):
\[ x = \frac{100}{2}. \]
This gives us:
\[ x = 50. \]
Conclusion
The value of \( x \) is
\[ \boxed{50}. \]
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