Answer:
Yusuf's mistake is in Step 1 of his solution.
Yusuf incorrectly added 2 to both sides of the equation, instead of subtracting it.
The correct step would be to subtract 2 from both sides:
\(\frac{1}{4}r + 2 - 2 = 10 - 2\)
Simplified into:
\(\frac{1}{4}r = 8\)
By changing the addition to subtraction, the equation would have been correctly set up for further solving.
The correct solution is \(r = 32\).
Explanation:
Given: \(\frac{1}{4}r + 2 = 10\)
Steps:
Step 1: Subtract 2 from both sides of the equation to isolate the term with "r":
\(\frac{1}{4}r = 10 - 2\)
Simplifying:
\(\frac{1}{4}r = 8\)
Step 2: Solve for "r" by multiplying both sides by 4 to eliminate the fraction:
\(4 \cdot \frac{1}{4}r = 4 \cdot 8\)
Simplifying:
\(r = 32\)
Conclusion: Yusuf's mistake was adding 2 instead of subtracting it in Step 1. By subtracting, we correctly obtain the solution \(r = 32\).