To solve the equation \( 5x + 8 + x = 32 \), we will follow these steps:
Step 1: Combine like terms.
The equation has two terms with \( x \): \( 5x \) and \( x \). We can combine them:
\[ 5x + x = 6x \]
Now, the equation simplifies to:
\[ 6x + 8 = 32 \]
Step 2: Isolate the variable term.
Next, we want to isolate the term with \( x \). We can do this by subtracting 8 from both sides of the equation:
\[ 6x + 8 - 8 = 32 - 8 \]
This simplifies to:
\[ 6x = 24 \]
Step 3: Solve for \( x \).
Now, divide both sides of the equation by 6:
\[ x = \frac{24}{6} \]
This simplifies to:
\[ x = 4 \]
Step 4: Check the solution.
Now, we will verify our solution by substituting \( x = 4 \) back into the original equation:
The original equation is:
\[ 5x + 8 + x = 32 \]
Substituting \( x = 4 \):
\[ 5(4) + 8 + 4 = 32 \]
Calculate the left-hand side:
\[ 20 + 8 + 4 = 32 \]
Now we add:
\[ 20 + 8 = 28 \] \[ 28 + 4 = 32 \]
Since both sides of the equation are equal (32 = 32), our solution is confirmed.
Final Answer:
\[ x = 4 \]