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:  In which step, if any, did Mariya make a mistake? (1 point) Responses Step 2 Step 2 No mistake found No mistake found Step 1 Step 1 Step 3

Answer 1

Mariya made a mistake in Step 1.

In the original problem \( a - 26 \leq -8 \), multiplying both sides by \(-26\) would reverse the inequality sign, making it:

\[ -26(a - 26) \geq -8(-26) \]

Instead, Mariya incorrectly states:

\[ (-26)(a - 26) \geq -8(-26) \]

The correct interpretation should have been:

\[ a - 26 \leq -8 \implies -26(a - 26) \geq 208, \]

which would then lead to:

\[ a \geq 208. \]

However, this leads to the conclusion that there was initially a misunderstanding of inequality signs when multiplying by a negative number.

Therefore, in response to your question, the mistake was in Step 1.