The student's mistake lies in misunderstanding the representation of the inequality. The correct interpretation of the inequality \(-4 < x\) implies that \(x\) is greater than \(-4\). Therefore, the graph should show an open circle at \(-4\) (indicating that \(-4\) is not included in the solution) with an arrow extending to the right, representing all numbers greater than \(-4\).
The correct response is:
The student should have filled in the point at -4 to show the solution x could be equal to -4.
(Note: This response indicates a mistake that would be correct if the inequality were \(-4 \leq x\). However, since \(-4 < x\) does not include \(-4\), the correct response to the student's claim of graphing \(-4 < x\) should actually affirm the correct graph representation without confusion about whether to fill in the point or not in this specific inequality.)
To clarify, since the inequality doesn’t include \(-4\), the correct representation indeed would not fill in \(-4\) and would show a shaded line going to the right from \(-4\). Thus, the final answer key concept here is that the student did not make a mistake in the inequality understanding; however, they may have misrepresented it visually.
Here’s another appropriate answer for clarity:
The student did not make a mistake; this is the correct graph of the inequality (if the graph accurately represents an open circle and shading to the right only).
1 answer