Let's solve the equation:

\[
\frac{1}{3}x + \frac{2}{5}x + 32 = x
\]

### Step 1: Combine like terms
The left-hand side of the equation has two terms with \(x\). To combine them, we need to find a common denominator between \(\frac{1}{3}\) and \(\frac{2}{5}\).

The least common denominator (LCD) of 3 and 5 is 15. So:

\[
\frac{1}{3}x = \frac{5}{15}x
\]
\[
\frac{2}{5}x = \frac{6}{15}x
\]

Now, combine the fractions:

\[
\frac{5}{15}x + \frac{6}{15}x = \frac{11}{15}x
\]

So the equation becomes:

\[
\frac{11}{15}x + 32 = x
\]

### Step 2: Move all terms involving \(x\) to one side
Subtract \(\frac{11}{15}x\) from both sides to get the \(x\)-terms on one side:

\[
32 = x - \frac{11}{15}x
\]

On the right-hand side, we can write \(x\) as \(\frac{15}{15}x\), so:

\[
32 = \frac{15}{15}x - \frac{11}{15}x
\]

This simplifies to:

\[
32 = \frac{4}{15}x
\]

### Step 3: Solve for \(x\)
Now, multiply both sides of the equation by 15 to eliminate the denominator:

\[
32 \times 15 = 4x
\]

\[
480 = 4x
\]

Finally, divide by 4 to solve for \(x\):

\[
x = \frac{480}{4} = 120
\]

### Solution:
The value of \(x\) is \( \boxed{120} \).

---

Do you want more details on any step or have any questions? 

Here are 5 related questions to practice:
1. Solve: \( \frac{2}{3}x + \frac{4}{5}x + 15 = x \)
2. Solve: \( 3x + 2 = 5x - 7 \)
3. Solve: \( \frac{5}{4}x + \frac{7}{6}x = x + 10 \)
4. Solve: \( x - \frac{3}{7}x = 20 \)
5. Solve: \( \frac{2}{3}x + 7 = x - 2 \)

**Tip:** When combining fractions, always remember to find the least common denominator for easy simplification.

Step-by-step solution for the linear equation 1/3x + 2/5x + 32 = x. This problem involves adding fractions with different denominators and solving for x. Learn how to combine like terms, find a common denominator, and solve linear equations. Suitable for students in Grades 7-9.

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