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

### Step 1: Eliminate the fraction
Multiply both sides of the equation by 3 to get rid of the fraction:

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

\[
15x + 1 = 21
\]

### Step 2: Isolate the term with \(x\)
Subtract 1 from both sides of the equation:

\[
15x = 21 - 1
\]

\[
15x = 20
\]

### Step 3: Solve for \(x\)
Divide both sides by 15:

\[
x = \frac{20}{15}
\]

Simplify the fraction:

\[
x = \frac{4}{3}
\]

### Final Answer: 
\[
x = \frac{4}{3}
\]

Would you like more details on any step?

Here are some related questions you can explore:
1. How do you solve equations with fractions and variables?
2. What is the process for simplifying fractions?
3. How can you check the solution of an equation?
4. What are other methods to solve linear equations?
5. How do you solve more complex equations with multiple variables?

**Tip:** Always simplify fractions as much as possible when solving equations.

Learn how to solve the linear equation 5x + 1/3 = 7 step-by-step. This guide covers key algebraic concepts, including eliminating fractions and isolating variables, suitable for students in Grades 6-8.

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