To simplify the expression \( 12 \frac{5}{8}x - 14x + \frac{1}{6}x \), let's proceed step by step.

### Step 1: Convert the mixed number into an improper fraction
The term \( 12 \frac{5}{8}x \) can be rewritten as an improper fraction:
\[
12 \frac{5}{8}x = \frac{101}{8}x
\]

Now the expression becomes:
\[
\frac{101}{8}x - 14x + \frac{1}{6}x
\]

### Step 2: Find a common denominator
To combine the terms, we need to find a common denominator. The denominators here are 8, 1 (for \( 14x \)), and 6. The least common denominator (LCD) is 24.

- \( \frac{101}{8}x \) becomes \( \frac{303}{24}x \)
- \( -14x \) becomes \( -\frac{336}{24}x \)
- \( \frac{1}{6}x \) becomes \( \frac{4}{24}x \)

### Step 3: Combine the terms
Now, add the fractions:
\[
\frac{303}{24}x - \frac{336}{24}x + \frac{4}{24}x
\]

Combine the numerators:
\[
\frac{303 - 336 + 4}{24}x = \frac{-29}{24}x
\]

### Final Answer:
The simplified expression is:
\[
\frac{-29}{24}x
\]

Would you like further clarification or details on any of these steps?

Here are 5 related questions:
1. How do you convert a mixed number to an improper fraction?
2. How do you find the least common denominator (LCD) between fractions?
3. How do you subtract and add fractions with different denominators?
4. How do you deal with negative terms in algebraic expressions?
5. How can you factor expressions involving fractions?

**Tip:** When dealing with fractions in algebraic expressions, always find the least common denominator (LCD) to combine terms efficiently.

Simplify the algebraic expression 12 5/8x - 14x + 1/6x with this detailed step-by-step solution. Learn how to convert mixed numbers to improper fractions, find the least common denominator (LCD), and combine algebraic terms. Suitable for students in Grades 8-10.

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