To solve for \( x \) in the equation \( 5x + 8 + x = 32 \), we will follow these steps:
Step 1: Combine like terms
Combine the \( x \) terms on the left side of the equation:
\[ 5x + x = 6x \]
Thus, the equation can be rewritten as:
\[ 6x + 8 = 32 \]
Step 2: Isolate the variable term
Next, we subtract \( 8 \) from both sides to isolate the term with \( x \):
\[ 6x + 8 - 8 = 32 - 8 \] \[ 6x = 24 \]
Step 3: Solve for \( x \)
Now, divide both sides by \( 6 \):
\[ x = \frac{24}{6} \] \[ x = 4 \]
Step 4: Check your solution
To check if our solution \( x = 4 \) is correct, we can substitute \( 4 \) back into the original equation:
\[ 5(4) + 8 + 4 = 32 \]
Calculate the left side:
\[ 20 + 8 + 4 = 32 \] \[ 28 + 4 = 32 \] \[ 32 = 32 \]
Since both sides of the equation are equal, our solution is confirmed.
Thus, the solution to the equation \( 5x + 8 + x = 32 \) is
\[ \boxed{4} \]