To solve the linear equation \(5x + 8 + x = 32\), follow these steps:
Step 1: Combine like terms
First, combine \(5x\) and \(x\): \[ 5x + x = 6x \] So, the equation becomes: \[ 6x + 8 = 32 \]
Step 2: Isolate the variable term
Next, subtract 8 from both sides to isolate the term with \(x\): \[ 6x + 8 - 8 = 32 - 8 \] This simplifies to: \[ 6x = 24 \]
Step 3: Solve for \(x\)
Now, divide both sides by 6 to solve for \(x\): \[ x = \frac{24}{6} \] So, \[ x = 4 \]
Step 4: Check your answer
To check if \(x = 4\) is correct, substitute \(4\) back into the original equation: \[ 5(4) + 8 + 4 = 32 \] Calculating the left side: \[ 20 + 8 + 4 = 32 \] Combining these: \[ 32 = 32 \]
Since both sides of the equation are equal, our solution is confirmed.
Conclusion
The solution to the equation \(5x + 8 + x = 32\) is: \[ \boxed{4} \]