Carlos made a mistake in the step after he modified the equation from \(5x + 7.5 = 25\) to \(5x = 32.5\). The correct steps for solving the equation should be as follows:
Starting with the original equation: \[ 5x + 7.5 = 25 \]
The first step should be to isolate \(5x\) by subtracting \(7.5\) from both sides: \[ 5x = 25 - 7.5 \] Calculating the right side gives: \[ 5x = 17.5 \]
Then, to solve for \(x\), divide both sides by \(5\): \[ x = \frac{17.5}{5} = 3.5 \]
So, the correct solution is \(x = 3.5\), not \(6.5\).
To check his solution, Carlos could substitute his answer back into the original equation: \[ 5(6.5) + 7.5 = 25 \] Calculating the left side: \[ 32.5 + 7.5 = 40 \] Since \(40 \neq 25\), this indicates that \(x = 6.5\) is not a correct solution.
Instead, if he substituted \(x = 3.5\): \[ 5(3.5) + 7.5 = 25 \] Calculating the left side: \[ 17.5 + 7.5 = 25 \] Since \(25 = 25\), this confirms that \(x = 3.5\) is indeed the correct solution.