A student claims that graph below represents the solutions to the inequality: −4<x
What was the student's mistake?
(1 point)
Responses
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
The student should have filled in the point at -4 to show the solution x could be equal to -4
The student should have multiplied by a negative and switched the direction of the arrow on the graph to go right instead of left
The student did not make a mistake; this is the correct graph of the inequality
The student's mistake is: 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.
The student's mistake is option 1: "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."
To explain why this is incorrect, let's analyze the inequality −4<x. The inequality states that x is greater than -4.
In terms of the number line, this means that the graph should represent all values of x that are greater than -4. The number line should be shaded to the right of -4 since that is the region that satisfies the inequality. The arrow should point towards the right.
However, the student made the mistake of shading the left side of -4 instead of the right side. This would imply that the solutions are values less than -4, which contradicts the original inequality. This is why the student's graph is incorrect.
The student's mistake is:
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.
This means that the correct inequality should be x > -4 instead of -4 < x. The student incorrectly labeled the direction of the inequality.