A student claims that graph below represents the solutions to the inequality: −4<x

Question

whats the mistake?

A. The student should have multiplied by a negative and switched the direction of the arrow on the graph to go right instead of left

B. The student did not make a mistake; this is the correct graph of the inequality

C. The student should have filled in the point at -4 to show the solution x could be equal to -4

D. The student did x is less than -4, when the variable is on the other side; -4 is less than x so x is greater than -4

Answer 1

The correct answer is:

B. The student did not make a mistake; this is the correct graph of the inequality.

The inequality \(-4 < x\) can be rewritten as \(x > -4\), which means that the solution includes all values greater than \(-4\). The graph would indeed show an open circle at \(-4\) (indicating that \(-4\) is not included) and shading to the right, indicating all values greater than \(-4\). Thus, the student's claim is accurate, and there is no mistake regarding the representation of the inequality on the graph.