Let's solve the equation step by step:

$\frac{1}{2}x - \frac{1}{4} + 10 = 5$

Step 1: Isolate the terms involving $x$

Subtract 10 from both sides:

$\frac{1}{2}x - \frac{1}{4} = 5 - 10$

$\frac{1}{2}x - \frac{1}{4} = -5$

Step 2: Eliminate the fraction involving $x$

Add $\frac{1}{4}$ to both sides:

$\frac{1}{2}x = -5 + \frac{1}{4}$

Step 3: Simplify the right side

Convert $-5$ to a fraction with denominator 4:

$-5 = \frac{-20}{4}$

Now, add the fractions:

$\frac{1}{2}x = \frac{-20}{4} + \frac{1}{4} = \frac{-19}{4}$

Step 4: Solve for $x$

Multiply both sides by 2 to eliminate the fraction:

$x = 2 \times \frac{-19}{4} = \frac{-38}{4} = \frac{-19}{2}$

Thus, the solution is:

$x = \frac{-19}{2}$

Would you like more details or have any questions?

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Here are 5 related questions:

1. How do you convert improper fractions to mixed numbers?
2. How do you handle equations with multiple fractions?
3. How do you solve equations with variables on both sides?
4. What happens when there are multiple variables in an equation?
5. How can you check if your solution is correct?

Tip: Always simplify fractions when possible to make calculations easier.