Question

mariya was asked to solve \\(\frac{a}{-13} \leq -16\\) and then graph the solution. her work is shown below.

step	mariyas work
step 1	\\((-13)\frac{a}{-13} \geq -16(-13)\\)
step 2	\\(a \geq 208\\)

| step 3 | <img src=\https://via.placeholder.com/150x30?text=205+206+207+208+209+210+211\ alt=
umber line from 205 to 211 with an open circle at 208 and a line to the right\> |
in which step, if any, did mariya make a mistake in her work?

Explanation:

Step1: Recall inequality rule

When multiplying/dividing an inequality by a negative number, the inequality sign flips. Here, we multiply both sides of \(\frac{a}{-13} \leq -16\) by \(-13\) (negative), so the sign should flip from \(\leq\) to \(\geq\). Step 1 does this correctly: \((-13)\frac{a}{-13} \geq -16(-13)\).

Step2: Check Step 2 calculation

Calculate \(-16 \times -13\). Since \((-16)\times(-13)=208\), and simplifying left side gives \(a\), so \(a \geq 208\) is correct.

Step3: Analyze Step 3 graph

The solution is \(a \geq 208\), which means the graph should have a closed circle at \(208\) (since \(a\) can equal \(208\)) and an arrow to the right. But Mariya's graph has an open circle at \(208\), which is a mistake. So Step 3 is incorrect.

Answer:

Step 3