To solve the equation \( 5x + 8 + x = 32 \), follow these steps:
Step 1: Combine like terms
Combine the \( x \) terms on the left side of the equation:
\[ 5x + x = 6x \]
So the equation becomes:
\[ 6x + 8 = 32 \]
Step 2: Isolate the term with \( x \)
Subtract 8 from both sides of the equation to isolate the term with \( x \):
\[ 6x + 8 - 8 = 32 - 8 \]
This simplifies to:
\[ 6x = 24 \]
Step 3: Solve for \( x \)
Now, divide both sides by 6 to solve for \( x \):
\[ x = \frac{24}{6} \]
This simplifies to:
\[ x = 4 \]
Step 4: Check the solution
To check the solution, substitute \( x = 4 \) back into the original equation:
The original equation is:
\[ 5x + 8 + x = 32 \]
Substituting in \( x = 4 \):
\[ 5(4) + 8 + 4 = 32 \]
Calculating the left side:
\[ 20 + 8 + 4 = 32 \]
Combine the numbers:
\[ 20 + 8 = 28 \] \[ 28 + 4 = 32 \]
Since both sides of the equation are equal (32 = 32), our solution is confirmed.
Thus, the final answer is:
\[ \boxed{4} \]