To solve the equation \( \frac{5x}{6} + \frac{1}{3} = \frac{7}{12} \), follow these steps:

### Step 1: Eliminate the fractions by finding a common denominator.
The denominators in the equation are 6, 3, and 12. The least common multiple (LCM) of 6, 3, and 12 is 12. Multiply every term by 12 to eliminate the fractions:

\[
12 \times \left(\frac{5x}{6}\right) + 12 \times \left(\frac{1}{3}\right) = 12 \times \left(\frac{7}{12}\right)
\]

### Step 2: Simplify the equation.
Perform the multiplication:

\[
2 \times 5x + 4 \times 1 = 7
\]

This simplifies to:

\[
10x + 4 = 7
\]

### Step 3: Isolate the variable term.
Subtract 4 from both sides of the equation:

\[
10x = 3
\]

### Step 4: Solve for \( x \).
Divide both sides by 10:

\[
x = \frac{3}{10}
\]

So, the solution is \( x = \frac{3}{10} \) or \( x = 0.3 \).

Would you like more details or have any questions?

### Related Questions:
1. How do you solve similar equations with different denominators?
2. What are the steps to find the least common multiple of two or more numbers?
3. How do you solve equations with variables on both sides?
4. What happens if the equation has a negative coefficient for the variable?
5. Can you solve equations involving fractions without finding a common denominator?

### Tip:
When solving equations with fractions, multiplying through by the least common multiple of the denominators can simplify the process significantly.

Discover how to solve the linear equation 5x/6 + 1/3 = 7/12 by eliminating fractions through the least common multiple (LCM) and isolating the variable x. This problem is ideal for students in Grades 6-8, focusing on key algebraic concepts and techniques for handling fractions in equations.

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