To solve the linear equation \( 5x + 8 + x = 32 \), we will follow these steps:
Step 1: Combine like terms
First, simplify the left side of the equation: \[ 5x + x = 6x \] Thus, the equation becomes: \[ 6x + 8 = 32 \]
Step 2: Isolate the variable term
Next, we want to isolate the term containing \( x \). To do this, subtract 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 by 6 to solve for \( x \): \[ x = \frac{24}{6} \] This simplifies to: \[ x = 4 \]
Step 4: Check the solution
To ensure that our solution is correct, we can substitute \( x = 4 \) back into the original equation: \[ 5(4) + 8 + 4 = 32 \] Simplifying the left side: \[ 20 + 8 + 4 = 32 \] Combining the numbers gives: \[ 28 + 4 = 32 \] Which simplifies to: \[ 32 = 32 \]
Since both sides of the equation are equal, our solution is confirmed.
Final Solution
Thus, the solution to the equation \( 5x + 8 + x = 32 \) is: \[ \boxed{4} \]