To solve the equation \( \frac{1}{4} + \frac{1}{2} x = 4 \), we can follow these steps:
- Subtract \( \frac{1}{4} \) from both sides:
\[ \frac{1}{2}x = 4 - \frac{1}{4} \]
- To perform the subtraction on the right side, convert 4 to a fraction with the same denominator:
\[ 4 = \frac{16}{4} \]
Now we can do the subtraction:
\[ 4 - \frac{1}{4} = \frac{16}{4} - \frac{1}{4} = \frac{15}{4} \]
So, the equation now looks like this:
\[ \frac{1}{2} x = \frac{15}{4} \]
- To isolate \( x \), multiply both sides by 2:
\[ x = 2 \times \frac{15}{4} \]
- Multiply:
\[ x = \frac{30}{4} \]
- Simplify the fraction:
\[ x = \frac{15}{2} \]
Thus, the solution to the equation is:
\[ \boxed{\frac{15}{2}} \]
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