Question
Mariya was asked to solve a/-26 ≤ -8 and graph and solution. Her work shown below.
Original Problem: a/-26 ≤ -8
Step 1: (-26) (a/-26) ≥ -8 (-26)
Step 2: a ≥ 208
Step 3: Ploted number graph of open 208 going to the right
In which step, if any, did Mariya make a mistake?
A. Step 1
B. No mistake found
C. Step 2
D. Step 3
Original Problem: a/-26 ≤ -8
Step 1: (-26) (a/-26) ≥ -8 (-26)
Step 2: a ≥ 208
Step 3: Ploted number graph of open 208 going to the right
In which step, if any, did Mariya make a mistake?
A. Step 1
B. No mistake found
C. Step 2
D. Step 3
Answers
Answered by
GPT-4o mini
Mariya made a mistake in Step 1.
In the original inequality \( \frac{a}{-26} \leq -8 \), when you multiply both sides by -26, you must reverse the inequality sign. Therefore, the correct transformation should be:
\[
(-26) \left(\frac{a}{-26}\right) \geq (-8)(-26)
\]
This leads to:
\[
a \geq 208
\]
While the calculation of \( (-8)(-26) \) is correct in obtaining 208, the sign change due to the multiplication by a negative number should have been addressed in the context of the inequality.
Thus, Mariya made a mistake in Step 1.
The answer is **A. Step 1**.
In the original inequality \( \frac{a}{-26} \leq -8 \), when you multiply both sides by -26, you must reverse the inequality sign. Therefore, the correct transformation should be:
\[
(-26) \left(\frac{a}{-26}\right) \geq (-8)(-26)
\]
This leads to:
\[
a \geq 208
\]
While the calculation of \( (-8)(-26) \) is correct in obtaining 208, the sign change due to the multiplication by a negative number should have been addressed in the context of the inequality.
Thus, Mariya made a mistake in Step 1.
The answer is **A. Step 1**.