inequalities

Question 1

what are the three ways we can represent an inequality

Answer 1

number line
set notation
interval notation

Question 2

how to represent an inequality on a number line

Answer 2

a shaded in dot means the inequality could be equal to it as well so it could be included

unshaded dot means that the inequality does not include the number (its just less than or greater than)

the number line goes from negative infinity to positive infinity

Question 3

how to represent an inequality in set notation

Answer 3

basically the same as the normal written inequality but just add X: and curly brackets around it

eg 2<X<8 = {X: 2<X<8}

Question 4

how to represent an inequality in interval notation

Answer 4

you write XE then write the number furthest left on the number line but before you need to know which bracket to open with and close with
curved bracket= if the number is not included in the inequality (isnt equal to it) so INFINITY IS ALWAYS A CURVED
square bracket= if the number is included in the inequality (so it is equal to it - shaded in on the number line)
then just write the numbers on like co-ordinates really. with the number furthest left on the number line (smallest number) first

eg. 8<=x<11 = XE [8,11)

Question 5

what to do if we have multiple regions on our inequality

Answer 5

eg we have x<-5 OR X>=9

we just write them both normally whether that’s in set or interval notation then just use U in-between

interval:
XE (-INFINITY,-5)U[9,INFINITY)