Question

​A student claims the graph below represents the solutions to the inequality −4 < x with this graph:





What was the student's mistake?

Responses

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

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

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

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 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.**

In this case, the graph should correctly show that the solutions to the inequality \( -4 < x \) (or equivalently, \( x > -4 \)) represent all values to the right of -4, which means the arrow should be pointing right and not left. The endpoint at -4 should also be left open (not filled in) since the inequality does not include -4 (it is strict, represented by the "<" symbol).