To solve the linear equation \(5x + 8 + x = 32\), let's follow the steps one by one.
Step 1: Combine like terms
First, we combine the \(x\) terms on the left side of the equation. We have \(5x\) and \(x\), which can be combined: \[ 5x + x = 6x \] So the equation now looks like this: \[ 6x + 8 = 32 \]
Step 2: Isolate the variable
Next, we want to get \(x\) by itself. To do that, we need to get rid of the \(8\) on the left side. 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 we will divide both sides of the equation by \(6\) to solve for \(x\): \[ x = \frac{24}{6} \] So, \[ x = 4 \]
Step 4: Check the solution
To check if our solution is correct, we can substitute \(x = 4\) back into the original equation: \[ 5x + 8 + x = 32 \] Substituting in \(x = 4\): \[ 5(4) + 8 + 4 = 32 \] Calculating \(5(4)\): \[ 20 + 8 + 4 = 32 \] Now we combine those: \[ 20 + 8 = 28 \] Then add \(4\): \[ 28 + 4 = 32 \] So, both sides of the equation are equal, which means our solution is correct.
Final Answer
Thus, the solution to the equation \(5x + 8 + x = 32\) is: \[ \boxed{4} \]