To solve the equation \( \frac{1}{3}x - 1 = 8 \), let's go step by step:

### Step 1: Isolate the term with \(x\).
First, add 1 to both sides of the equation:
\[
\frac{1}{3}x - 1 + 1 = 8 + 1
\]
\[
\frac{1}{3}x = 9
\]

### Step 2: Eliminate the fraction.
Multiply both sides of the equation by 3 to cancel out the denominator:
\[
3 \times \frac{1}{3}x = 3 \times 9
\]
\[
x = 27
\]

### Final Answer:
\[
x = 27
\]

Would you like further details or have any questions?

Here are 5 related questions for practice:
1. Solve \( \frac{2}{5}x - 4 = 6 \).
2. What is \( 2x - 3 = 11 \)?
3. Solve \( \frac{1}{4}x + 2 = 10 \).
4. How do you solve \( \frac{3}{2}x - 5 = 7 \)?
5. Solve for \(x\) in \( 5x + 6 = 31 \).

**Tip:** Always perform the same operation on both sides of an equation to maintain balance.

Learn how to solve the linear equation 1/3x - 1 = 8 with a detailed, step-by-step breakdown. This problem covers fundamental algebraic concepts such as isolating variables and eliminating fractions. Ideal for students in Grades 6-8.

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