To solve the equation \( 5x + 8 + x = 32 \), we will follow these steps:
Step 1: Combine like terms
First, we combine the terms involving \( x \).
\[ 5x + x = 6x \] 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.
\[ 6x + 8 - 8 = 32 - 8 \] This simplifies to: \[ 6x = 24 \]
Step 3: Solve for \( x \)
Now, divide both sides by 6 to solve for \( x \).
\[ x = \frac{24}{6} \] Thus, \[ x = 4 \]
Step 4: Check the solution
To ensure our solution is correct, we will substitute \( x = 4 \) back into the original equation.
The original equation is: \[ 5x + 8 + x = 32 \]
Substituting \( x = 4 \): \[ 5(4) + 8 + 4 = 32 \] Calculating: \[ 20 + 8 + 4 = 32 \] Then: \[ 28 + 4 = 32 \] And: \[ 32 = 32 \]
Since both sides of the equation are equal, our solution is verified.
Final Answer
The solution to the equation \( 5x + 8 + x = 32 \) is: \[ \boxed{4} \]
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