Please enable JavaScript.
Coggle requires JavaScript to display documents.
Compound Linear Inequalities (Important Properties (Additive Inverse (For…
Compound Linear Inequalities
Important Properties
Additive Inverse
For any real numbers a and b: If a > b, then -a < -b
Multiplicative Inverse
For any real numbers a and b, that are both positive or both negative: If a > b, then 1/a < 1/b
Display
Interval Notation
Open Interval
(a,b)
a < x < b
Half-open Interval
(a,b]
a < x ≤ b
Half-closed Interval
[a,b)
a ≤ x < b
Closed Interval
[a,b]
a ≤ x ≤ b
Set Notation
An example would be: {x ∈ R : a < x < b}
a < x < b
"AND" & "OR"
For the "and" condition, the solution corresponds to the interval that all the number lines pass through
For the "or" condition, the solution set corresponds to the interval(s) that any (at least one) of the lines pass through