Let's carefully analyze Tobin's work to identify any mistakes.
1. Original Equation:
[tex]\[
3(x - 1.25) = 11.25
\][/tex]
2. Distribute the 3 correctly:
[tex]\[
3(x - 1.25) = 3 \cdot x - 3 \cdot 1.25 = 3x - 3.75
\][/tex]
Now the equation is:
[tex]\[
3x - 3.75 = 11.25
\][/tex]
3. Add 3.75 to both sides to isolate the term with [tex]\( x \)[/tex]:
[tex]\[
3x - 3.75 + 3.75 = 11.25 + 3.75
\][/tex]
This simplifies to:
[tex]\[
3x = 15
\][/tex]
4. Tobin's mistake occurred in the next step. He incorrectly multiplied by 3 instead of dividing by 3 to solve for [tex]\( x \)[/tex]:
[tex]\[
3x \cdot 3 = 45.3 \text{ (incorrect)} \Rightarrow x = 135 \text{ (incorrect)}
\][/tex]
Instead, Tobin should have divided both sides by 3:
[tex]\[
\frac{3x}{3} = \frac{15}{3}
\][/tex]
Simplifying this gives:
[tex]\[
x = 5
\][/tex]
Therefore, the mistake Tobin made was not dividing by 3 correctly in the final step. Instead, he mistakenly multiplied by 3. Thus, the correct statement is:
Tobin should have divided by 3.
This explains why the final values obtained by Tobin were incorrect.
