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: Closed circle starting from 6 passing 11

In which step, if any, did Mariya make a mistake?

(1 point)
Responses

Step 3
Step 3

Step 1
Step 1

Step 2
Step 2

No mistake found
No mistake found

Answer 1

Mariya made a mistake in **Step 1**. Here’s the breakdown of the problem:

The original inequality is \( a - 2 \geq -3 \).

1. To solve for \( a \), you need to add 2 to both sides of the inequality:
\[
a - 2 + 2 \geq -3 + 2 \implies a \geq -1
\]

2. In Mariya's Step 1, she incorrectly multiplied both sides of the inequality by -2, which is unnecessary and incorrectly impacts the direction of the inequality.

3. In Step 2, she states \( a \geq 6 \), which is incorrect. The correct inequality should be \( a \geq -1 \).

4. In Step 3, she also incorrectly describes the graph.

So the answer is that Mariya made a mistake in **Step 1**.