Question
Mariya was asked to solve a−26≤−8
and graph the solution. Her work is shown below.
Original Problem: a−26≤−8
Step 1: (−26) (a/−26) ≥ −8 (−26)
Step 2: a ≥ 208
Step 3: 205 206 207 208 209 210 211
In which step, if any, did Mariya make a mistake?
(1 point)
Responses
Step 2
Step 2
Step 1
Step 1
Step 3
Step 3
No mistake found
No mistake found
and graph the solution. Her work is shown below.
Original Problem: a−26≤−8
Step 1: (−26) (a/−26) ≥ −8 (−26)
Step 2: a ≥ 208
Step 3: 205 206 207 208 209 210 211
In which step, if any, did Mariya make a mistake?
(1 point)
Responses
Step 2
Step 2
Step 1
Step 1
Step 3
Step 3
No mistake found
No mistake found
Answers
Answered by
GPT-4o mini
Mariya made a mistake in Step 1.
In her first step, she incorrectly manipulated the inequality. When multiplying or dividing both sides of an inequality by a negative number, the direction of the inequality must be reversed.
The correct process is:
1. Start with the original inequality: \( a - 26 \leq -8 \)
2. Add 26 to both sides to isolate \( a \):
\[ a \leq -8 + 26 \]
\[ a \leq 18 \]
So the correct final inequality is \( a \leq 18 \), not \( a \geq 208 \) as she concluded in Step 2.
Thus, the correct response is:
**Step 1**
In her first step, she incorrectly manipulated the inequality. When multiplying or dividing both sides of an inequality by a negative number, the direction of the inequality must be reversed.
The correct process is:
1. Start with the original inequality: \( a - 26 \leq -8 \)
2. Add 26 to both sides to isolate \( a \):
\[ a \leq -8 + 26 \]
\[ a \leq 18 \]
So the correct final inequality is \( a \leq 18 \), not \( a \geq 208 \) as she concluded in Step 2.
Thus, the correct response is:
**Step 1**