Solve the following linear equation for x

To solve the equation \( 5x + 8 + x = 32 \), we will follow these steps:

### Step 1: Combine like terms
First, we combine the terms involving \( x \).

\[
5x + x = 6x
\]
So the equation becomes:
\[
6x + 8 = 32
\]

### Step 2: Isolate the variable term
Next, we need to isolate the term with \( x \) by subtracting 8 from both sides.

\[
6x + 8 - 8 = 32 - 8
\]
This simplifies to:
\[
6x = 24
\]

### Step 3: Solve for \( x \)
Now, divide both sides by 6 to solve for \( x \).

\[
x = \frac{24}{6}
\]
Thus,
\[
x = 4
\]

### Step 4: Check the solution
To ensure our solution is correct, we will substitute \( x = 4 \) back into the original equation.

The original equation is:
\[
5x + 8 + x = 32
\]

Substituting \( x = 4 \):
\[
5(4) + 8 + 4 = 32
\]
Calculating:
\[
20 + 8 + 4 = 32
\]
Then:
\[
28 + 4 = 32
\]
And:
\[
32 = 32
\]

Since both sides of the equation are equal, our solution is verified.

### Final Answer
The solution to the equation \( 5x + 8 + x = 32 \) is:
\[
\boxed{4}
\]