Question: Solve the equation below using inverse operations.
x - 4.25 = 7.5
Ozzy’s work
x - 4.25 = 7.5
+ 4.25 + 4.25
x = 11.85
Ozzy solved the equation shown. What do you notice?
He made a mistake when adding 7.5 and 4.25.
He solved the equation correctly.
He added 4.25 when he should have subtracted.
He should have subtracted 7.5 from both sides instead of adding 4.25.
1. **State the problem:** Solve the equation $$x - 4.25 = 7.5$$ using inverse operations and analyze Ozzy's solution.
2. **Formula and rule:** To isolate $$x$$, add $$4.25$$ to both sides because the equation subtracts $$4.25$$ from $$x$$. The inverse operation of subtraction is addition.
3. **Ozzy's work:**
$$
\begin{aligned}
x - 4.25 &= 7.5 \\
+4.25 \quad +4.25 \\
x &= 7.5 + 4.25 \\
x &= 11.75
\end{aligned}
$$
4. **Check Ozzy's addition:**
$$7.5 + 4.25 = 11.75$$, but Ozzy wrote $$11.85$$ which is incorrect.
5. **Conclusion:** Ozzy solved the equation correctly by adding $$4.25$$ to both sides, but he made a mistake in adding $$7.5$$ and $$4.25$$. The correct answer is $$x = 11.75$$.
6. **Answer to the multiple-choice:** "He made a mistake when adding 7.5 and 4.25."