-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.
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?
1 answer