Open Middle®
Directions: Create two inequalities that have the same number of solutions.
Hint
How can we determine how many solutions an inequality has?
How many solutions does each inequality have?
How many solutions does each inequality have?
Answer
All inequalities have an infinite number of solutions so any two inequalities should work.
There should still be good debate as to whether x < 3 and x < 4 have the same number of solutions.
Source: Robert Kaplinsky
Just a small correction: Not every inequality has an infinite number of solutions.
Over the integers, |x| x+1) with 0 solutions, which is even the subject of another Open Middle task that was posted before this one.
For some reason, some text disappeared again… I was trying to say:
Over the integers, the inequality “absolute value of x is less than 2” has 3 solutions. Now you might say “By inequality I mean linear inequalities with 1 variable, because that is what is taught in 6th grade”. But even then, there are inequalities (like x is greater than x + 1) with 0 solutions, which is even the subject of another Open Middle task that was posted before this one.
Other great discussion prompts:
*Are the number of solutions to 3<x<4 same/greater/less than the number of solutions to x<4?
*Are the number of solutions to x<4 the same/greater/less than the number of solutions to x<=4?
instead the problem should say: “make two inequalities where both inequalities have the exact same set of solutions. you cannot use the same inequality twice.”
this is a HUGE improvement, right?