Let's solve the equation:

\[
\frac{x}{16} - \frac{x - 2}{8} = 2
\]

### Step 1: Get rid of the denominators.
We can eliminate the fractions by multiplying both sides of the equation by 16, the least common multiple (LCM) of the denominators 16 and 8.

\[
16 \times \left( \frac{x}{16} \right) - 16 \times \left( \frac{x - 2}{8} \right) = 16 \times 2
\]

This simplifies to:

\[
x - 2(x - 2) = 32
\]

### Step 2: Simplify the equation.
Distribute the -2 to the terms inside the parentheses:

\[
x - 2x + 4 = 32
\]

Now combine like terms:

\[
-x + 4 = 32
\]

### Step 3: Solve for \( x \).
Subtract 4 from both sides:

\[
-x = 28
\]

Multiply both sides by -1:

\[
x = -28
\]

### Final Answer:
\[
x = -28
\]

Would you like further clarification or details on any step?

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Here are five related questions for further practice:
1. Solve \(\frac{y}{12} - \frac{y-3}{6} = 5\).
2. Solve \(\frac{x}{5} + \frac{x+1}{3} = 4\).
3. Solve \( \frac{x}{10} - \frac{2x - 5}{15} = 1 \).
4. Solve \( \frac{2x}{9} - \frac{x + 4}{6} = 3 \).
5. Solve \( \frac{x}{7} - \frac{x - 1}{14} = 1 \).

**Tip**: Multiplying by the least common multiple (LCM) of denominators helps clear fractions in equations efficiently!

Learn how to solve the linear equation x/16 - (x - 2)/8 = 2 by eliminating fractions using the least common multiple (LCM). This step-by-step guide simplifies algebraic fractions, making it ideal for students in Grades 8-10.

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