Mariya was asked to solve a−26≤−8

Question

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

Answer 1

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