To solve the equation \(\frac{1}{4}(2x + 1) = 26\), we can follow these steps:
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Eliminate the fraction by multiplying both sides of the equation by 4:
\[ 4 \cdot \frac{1}{4}(2x + 1) = 4 \cdot 26 \]
This simplifies to:
\[ 2x + 1 = 104 \]
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Subtract 1 from both sides:
\[ 2x + 1 - 1 = 104 - 1 \]
This simplifies to:
\[ 2x = 103 \]
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Divide both sides by 2:
\[ x = \frac{103}{2} = 51.5 \]
So, the solution to the equation is: \[ \boxed{51.5} \]