Question

1. explain the error in graphing the inequality.

(-17 < x - 14)
(-17 + 14 < x - 14 + 14)
(-3 < x)
number line with labels -6, -5, -4, -3, -2, -1, 0; open circle at -3; arrow pointing left

Explanation:

Step1: Analyze the inequality solution

First, let's solve the inequality \( - 17-3\)).

Step2: Analyze the number line graph

The inequality \(x > - 3\) means that we should shade the region to the right of \(x=-3\) on the number line. But in the given graph, the arrow is pointing to the left of \(-3\) (towards more negative numbers), which is the region for \(x < - 3\), not \(x>-3\). So the error is in the direction of the arrow on the number line. The graph should have an open circle at \(-3\) (since the inequality is strict, \(x
eq - 3\)) and the arrow should point to the right (towards positive numbers) to represent \(x>-3\), but instead, it points to the left (representing \(x < - 3\)).

Answer:

The solution to the inequality \( - 17-3\). The error in the graph is that the arrow is pointing to the left of \(-3\) (representing \(x < - 3\)) instead of to the right (which should represent \(x>-3\)). Also, the open circle is at \(-3\) (correct for the strict inequality), but the direction of the arrow is incorrect; it should point to the right to show all values of \(x\) greater than \(-3\).