Question
Mariya was asked to solve a−2≥−3
and graph the solution. Her work is shown below.
Original Problem: a−2≥−3
Step 1: (−2)(a−2)≥−3(−2)
Step 2: a≥6
Step 3: 1 2 3 4 5 6 7 8 9 10 11
(6-11)
In which step, if any, did Mariya make a mistake?
(1 point)
Responses
Step 1
Step 1
Step 2
Step 2
Step 3
Step 3
No mistake found
and graph the solution. Her work is shown below.
Original Problem: a−2≥−3
Step 1: (−2)(a−2)≥−3(−2)
Step 2: a≥6
Step 3: 1 2 3 4 5 6 7 8 9 10 11
(6-11)
In which step, if any, did Mariya make a mistake?
(1 point)
Responses
Step 1
Step 1
Step 2
Step 2
Step 3
Step 3
No mistake found
Answers
GPT-4o mini
Mariya made a mistake in **Step 1**.
The original inequality is:
\( a - 2 \geq -3 \)
To isolate \( a \), she should have added 2 to both sides rather than multiplying. The correct transformation would be:
Step 1:
\( a - 2 + 2 \geq -3 + 2 \)
This simplifies to:
\( a \geq -1 \)
In **Step 2**, she incorrectly concluded that \( a \geq 6 \) based on an incorrect manipulation. Therefore, the mistake is found in **Step 1**.
The original inequality is:
\( a - 2 \geq -3 \)
To isolate \( a \), she should have added 2 to both sides rather than multiplying. The correct transformation would be:
Step 1:
\( a - 2 + 2 \geq -3 + 2 \)
This simplifies to:
\( a \geq -1 \)
In **Step 2**, she incorrectly concluded that \( a \geq 6 \) based on an incorrect manipulation. Therefore, the mistake is found in **Step 1**.