Question

Describe how you know if an inequality is an “and” or an “or” problem. (use -3 < x+5 < 8). Also, how do you know if an absolute value question is an “and” or an “or” problem?

Answer 1

-3 < x+5 < 8
subtract 5, (subtraction does not affect the direction of the inequality)
-8 < x < 3

This pattern implies the word "and"
- it can also be read:
x is between -8 and 3
- to have "between -8 and 3" mean: greater than -8 OR less than 3 would cover the entire number line, and any x would work, but clearly that would be a contradiction, so ....

As to absolute value:
|stuff| < k , where k is a positive number
stuff < k and -stuff < k
stuff < k and stuff > -k
or -k < stuff < k ,

|stuff| > k
stuff > k OR -stuff > k
stuff > k OR stuff < -k

stuff < -k OR stuff > k

I used to have my students remember that
"greater" sounds like "greatOR", and once you have established one choice, the other one is obvious.