https://file.aiquickdraw.com/mathbot/file/1726885146041mcdwhdun.jpg

Let's solve the equation from the image:

The given equation is:

\[
x - \frac{1}{4} = \frac{1}{2}
\]

### Step 1: Isolate \( x \)
To isolate \( x \), add \( \frac{1}{4} \) to both sides of the equation:

\[
x = \frac{1}{2} + \frac{1}{4}
\]

### Step 2: Add the fractions
To add the fractions, find a common denominator. The least common denominator of 2 and 4 is 4:

\[
\frac{1}{2} = \frac{2}{4}
\]

Now add:

\[
x = \frac{2}{4} + \frac{1}{4} = \frac{3}{4}
\]

### Final Answer:
\[
x = \frac{3}{4}
\]

So, the correct answer is the first option: \( x = \frac{3}{4} \).

Would you like further details or have any additional questions?

Here are 5 related questions to further explore this topic:
1. How do you solve equations with variables on both sides?
2. What happens when the equation has no solution?
3. How do you solve equations that contain decimals instead of fractions?
4. How can you check if your solution is correct?
5. Can you solve equations with fractions that have different denominators?

**Tip**: Always check your final answer by substituting it back into the original equation!

Learn how to solve the linear equation x - 1/4 = 1/2, step-by-step. Understand how to manipulate fractions and find the solution using algebraic techniques. Suitable for students in Grades 6-8.

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