Let's go through the steps of the equation that Carlos solved to identify the mistake he made.
The original equation is:
\[ 5x + 7.5 = 25 \]
To isolate \( x \), you would first subtract \( 7.5 \) from both sides:
\[ 5x = 25 - 7.5 \]
Calculating the right side:
\[ 25 - 7.5 = 17.5 \]
So, the equation should become:
\[ 5x = 17.5 \]
Next, you would divide both sides by \( 5 \):
\[ x = \frac{17.5}{5} \]
Now calculating \( \frac{17.5}{5} \):
\[ x = 3.5 \]
So, Carlos made a mistake in his subtraction. Instead of correctly calculating \( 25 - 7.5 \), he incorrectly got \( 32.5 \).
To check his solution, he could substitute his value of \( x \) back into the original equation:
-
Substitute \( x = 6.5 \) into the left side of the original equation:
\[ 5(6.5) + 7.5 = 32.5 + 7.5 = 40 \]
-
Then check if this equals \( 25 \):
Since \( 40 \neq 25 \), Carlos would see that his answer was incorrect.
By substituting his solution back into the original equation, he would have recognized that \( x = 6.5 \) was not a valid solution, leading him to re-evaluate his calculations.