We are given the equation:

\[
\frac{1}{3}(x - 15) = x + 27
\]

To solve for \(x\), follow these steps:

### Step 1: Eliminate the fraction
Multiply both sides of the equation by 3 to eliminate the denominator on the left-hand side.

\[
3 \times \frac{1}{3}(x - 15) = 3 \times (x + 27)
\]

This simplifies to:

\[
x - 15 = 3(x + 27)
\]

### Step 2: Distribute the 3 on the right-hand side
Now distribute the 3 on the right-hand side:

\[
x - 15 = 3x + 81
\]

### Step 3: Move all \(x\)-terms to one side
Subtract \(x\) from both sides to get the \(x\)-terms on one side of the equation:

\[
x - 15 - x = 3x + 81 - x
\]

This simplifies to:

\[
-15 = 2x + 81
\]

### Step 4: Isolate the \(x\)-term
Now, subtract 81 from both sides:

\[
-15 - 81 = 2x
\]

This simplifies to:

\[
-96 = 2x
\]

### Step 5: Solve for \(x\)
Divide both sides by 2:

\[
x = \frac{-96}{2}
\]

\[
x = -48
\]

### Final Answer:
\[
x = -48
\]

Would you like any further clarification or details on this solution?

Here are 5 related questions to deepen your understanding:
1. How do you handle equations with fractions on both sides?
2. What happens if the fraction has a different denominator?
3. How can you verify the solution of an equation?
4. How do you solve an equation with multiple terms in the numerator?
5. What is the effect of distributing a negative number across parentheses?

**Tip:** Always clear fractions early in an equation to simplify your calculations!

Learn how to solve the linear equation 1/3(x-15) = x + 27 step-by-step. This guide demonstrates how to eliminate fractions, use the distributive property, and solve for x. Ideal for students in Grades 8-10.

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