To solve the equation \( 5x + 8 + x = 32 \), follow these steps:
Step 1: Combine like terms
First, combine the \( x \) terms on the left side of the equation:
\[ 5x + x = 6x \]
Thus, 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:
\[ 6x + 8 - 8 = 32 - 8 \]
This simplifies to:
\[ 6x = 24 \]
Step 3: Solve for \( x \)
Now we can solve for \( x \) by dividing both sides by 6:
\[ x = \frac{24}{6} \]
This simplifies to:
\[ x = 4 \]
Step 4: Check your solution
To verify our solution, we will substitute \( x = 4 \) back into the original equation:
Original equation:
\[ 5x + 8 + x = 32 \]
Substituting \( x = 4 \):
\[ 5(4) + 8 + 4 = 32 \]
Now calculate:
\[ 20 + 8 + 4 = 32 \] \[ 32 = 32 \]
Since both sides of the equation are equal, our solution is confirmed to be correct.
Final Answer
\[ x = 4 \]