To solve the equation \(5x + 8 + x = 32\), we’ll follow these steps:
Step 1: Combine like terms
We can combine \(5x\) and \(x\):
\[ 5x + x = 6x \]
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 of the equation:
\[ 6x + 8 - 8 = 32 - 8 \]
Simplifying both sides gives:
\[ 6x = 24 \]
Step 3: Solve for \(x\)
Now, we can solve for \(x\) by dividing both sides of the equation by \(6\):
\[ x = \frac{24}{6} \]
This simplifies to:
\[ x = 4 \]
Step 4: Check the solution
To ensure our solution is correct, we can substitute \(x = 4\) back into the original equation:
Starting with the original equation:
\[ 5x + 8 + x = 32 \]
Substituting \(x = 4\):
\[ 5(4) + 8 + 4 = 32 \]
Calculating the left side,
\[ 20 + 8 + 4 = 32 \]
Simplifying further,
\[ 28 + 4 = 32 \]
Finally,
\[ 32 = 32 \]
Since both sides of the equation are equal, our solution \(x = 4\) is verified.
Conclusion
The solution to the equation \(5x + 8 + x = 32\) is
\[ \boxed{4} \]