Intervals, Inequalities, and Absolute Values

Appendix A -
Intervals , Inequalities ,
and Absolute 08/24/2022

Math 224



Intervals (we only use real numbers


Notation Set Description Picture

(a , b) Exa(x(b) A b
"Such
"
~ that




[a b] ,
(xa[x1b) ⑨

A ·


[a b) ,
(xazx(b) ⑳

C b




(a b] ,
(xa(x = b) C
⑧

b




(a c) ,
(xxa) A




[a c) ,
(xx(a) h


1 -
w
,
b) (xx(b3 b




1 -

0
,
b) Exx = b3 >
-
⑳

b




I-
x
,
c) R




Inequalities
Rules For Inequalities
1) If alb ,
then a+ c > b+




2) If Alb and Cd ,
then a+ c < b + d




3) If alb and 30
,
then a cab




4) If alb and Co then ac > bC
,




5) If Oca1b ,
then as



Solving Inequalities
Examples :




1)1 + x(7X + 5

-
4 + X < 7X

-

476X
-


<X
-


37X Interval Notation : (-33 8)
3
,
-