To solve the expression \(\frac{1}{6}x + \frac{1}{12}x + \frac{1}{7}x + \frac{1}{2}x\), we can first find a common denominator and then combine the fractions.

### Step 1: Identify the common denominator
The denominators are 6, 12, 7, and 2. The least common denominator (LCD) of these numbers is 84.

### Step 2: Rewrite each fraction with the common denominator
\[
\frac{1}{6}x = \frac{14}{84}x, \quad \frac{1}{12}x = \frac{7}{84}x, \quad \frac{1}{7}x = \frac{12}{84}x, \quad \frac{1}{2}x = \frac{42}{84}x
\]

### Step 3: Add the fractions
\[
\frac{14}{84}x + \frac{7}{84}x + \frac{12}{84}x + \frac{42}{84}x = \frac{14 + 7 + 12 + 42}{84}x = \frac{75}{84}x
\]

### Step 4: Simplify the fraction
\[
\frac{75}{84}x = \frac{25}{28}x
\]

So, the simplified form of the expression is \(\frac{25}{28}x\).

Would you like more details on any of these steps, or do you have any questions?

Here are 5 related questions to further explore this topic:
1. How do you find the least common denominator of multiple fractions?
2. Can you simplify the expression \(\frac{5}{14}x + \frac{3}{28}x\)?
3. How do you add fractions with different denominators?
4. What is the process for simplifying fractions after addition?
5. How would the solution change if the expression had different coefficients?

**Tip:** When adding fractions, always look for the least common denominator to simplify the calculation process.

Learn how to simplify the expression (1/6)x + (1/12)x + (1/7)x + (1/2)x step-by-step. Find the common denominator, rewrite each fraction, add them together, and simplify to (25/28)x. Suitable for Grades 6-8.

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