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)ResponsesStep 3Step 3No mistake foundNo mistake foundStep 1Step 1Step 2

Answer 1

Mariya made a mistake in Step 1. The original inequality is \( a - 26 \leq -8 \), and there is no need to multiply both sides by \(-26\). In fact, when you multiply or divide both sides of an inequality by a negative number, you need to reverse the inequality sign.

Here's the correct approach:

1. Start with the original inequality: \[ a - 26 \leq -8 \]

2. Add 26 to both sides: \[ a \leq -8 + 26 \] \[ a \leq 18 \]

So, the correct solution should be \( a \leq 18 \). Therefore, the mistake occurs in Step 1, where Mariya incorrectly manipulated the inequality.

The correct response is: Step 1.