To solve the equation:

\[
\frac{1}{12}x - \frac{1}{12} = \frac{1}{8}x + \frac{1}{6} - \frac{1}{6}x
\]

Let's start by combining like terms and isolating the variable \(x\).

### Step 1: Combine like terms
First, let's group all the terms with \(x\) on one side and the constant terms on the other side:

\[
\frac{1}{12}x - \frac{1}{8}x + \frac{1}{6}x = \frac{1}{6} + \frac{1}{12}
\]

### Step 2: Find a common denominator
To simplify, we need a common denominator for the fractions:

- For the \(x\)-terms: The least common multiple (LCM) of 12, 8, and 6 is 24.
- For the constants: The LCM of 6 and 12 is also 12.

Rewrite the equation with these denominators:

\[
\left( \frac{2}{24}x - \frac{3}{24}x + \frac{4}{24}x \right) = \left( \frac{2}{12} + \frac{1}{12} \right)
\]

### Step 3: Simplify the equation
Combine the like terms:

\[
\frac{(2 - 3 + 4)}{24}x = \frac{(2 + 1)}{12}
\]

\[
\frac{3}{24}x = \frac{3}{12}
\]

Simplify both sides:

\[
\frac{1}{8}x = \frac{

Learn how to solve the linear equation involving fractions: 1/12x - 1/12 = 1/8x + 1/6 - 1/6x. This step-by-step guide covers key algebraic concepts such as combining like terms, using common denominators, and solving for x. Suitable for students in Grades 8-10.

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