https://file.aiquickdraw.com/mathbot/file/172624179433331lhjrt1.jpg

The equation given is:

\[
\frac{x}{4} + \frac{7x}{6} = \, ?
\]

### Step 1: Find a common denominator
The denominators are 4 and 6. The least common denominator (LCD) between 4 and 6 is 12.

### Step 2: Rewrite the fractions with the common denominator
\[
\frac{x}{4} = \frac{3x}{12} \quad \text{(since \( \frac{x}{4} \times \frac{3}{3} = \frac{3x}{12} \))}
\]
\[
\frac{7x}{6} = \frac{14x}{12} \quad \text{(since \( \frac{7x}{6} \times \frac{2}{2} = \frac{14x}{12} \))}
\]

### Step 3: Add the two fractions
Now, add the fractions:
\[
\frac{3x}{12} + \frac{14x}{12} = \frac{(3x + 14x)}{12} = \frac{17x}{12}
\]

Thus, the simplified expression is:
\[
\frac{17x}{12}
\]

### Step 4: Solve for \( x \neq 0 \)
Since this is a fraction, \( x \) cannot be 0 because it would make the entire expression equal to 0. Therefore, \( x \neq 0 \).

The correct answer is:
\[
\frac{17x}{12}, \, x \neq 0
\]

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Would you like more details or have any further questions? 

Here are 5 related questions you can explore:
1. How do you find the least common denominator for two fractions?
2. How do you add fractions with different denominators?
3. What are some rules for simplifying fractions?
4. Can we solve for \(x\) if there were numbers on both sides of the equation?
5. How would this process change if there were subtraction instead of addition?

**Tip:** Always make sure to simplify your fractions whenever possible to make calculations easier.

Learn how to simplify the fractional expression x/4 + 7x/6 by finding the least common denominator and adding the fractions. This step-by-step guide is ideal for students in Grades 6-8 who are studying basic fraction operations.

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