To solve the equation \( 5x + 8 + x = 32 \), we first combine like terms on the left side.
Step 1: Combine like terms
The terms \( 5x \) and \( x \) can be combined: \[ 5x + x = 6x \] So the equation can be rewritten as: \[ 6x + 8 = 32 \]
Step 2: Isolate the variable
Next, we will isolate \( x \) by subtracting \( 8 \) from both sides: \[ 6x + 8 - 8 = 32 - 8 \] This simplifies to: \[ 6x = 24 \]
Step 3: Solve for \( x \)
Now, we divide both sides by \( 6 \) to solve for \( x \): \[ x = \frac{24}{6} \] So: \[ x = 4 \]
Step 4: Check the solution
To check the solution, we substitute \( x = 4 \) back into the original equation: \[ 5x + 8 + x = 32 \] Substituting \( x \): \[ 5(4) + 8 + 4 = 32 \] Calculating the left side: \[ 20 + 8 + 4 = 32 \] Simplifying that gives: \[ 32 = 32 \] 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: \[ \boxed{4} \]
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