We can solve the equation \( \frac{5x}{3} + \frac{1}{3} = 7 \) step by step:

### Step 1: Eliminate the denominators by multiplying the entire equation by 3 (the denominator).
\[
3 \times \left( \frac{5x}{3} + \frac{1}{3} \right) = 3 \times 7
\]
This simplifies to:
\[
5x + 1 = 21
\]

### Step 2: Subtract 1 from both sides to isolate the term with \(x\):
\[
5x = 21 - 1
\]
\[
5x = 20
\]

### Step 3: Divide both sides by 5 to solve for \(x\):
\[
x = \frac{20}{5}
\]
\[
x = 4
\]

Thus, the solution is \( x = 4 \).

Would you like further details or have any questions?

Here are 5 related questions to further explore:
1. What happens if we change the constant 7 to a different number?
2. How would you solve \( \frac{5x}{3} + \frac{1}{3} = 0 \)?
3. Can you solve \( \frac{7x}{2} + \frac{5}{4} = 10 \)?
4. How does solving fractions change when working with negative numbers?
5. How can you check if a solution is correct by substituting it back into the original equation?

**Tip:** Always multiply both sides by the least common denominator (LCD) to eliminate fractions early in solving!

Learn how to solve the linear equation 5x/3 + 1/3 = 7 step by step. This problem covers key algebraic concepts, including handling fractions and solving for x. Suitable for students in Grades 6-8.

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