How do you solve and write the following in interval notation: #x< 5# AND #x< 3#?

1 Answer
Mar 25, 2017

Answer:

#x < 3#
#x in (-oo,3)#

Explanation:

As can be seen in the diagram:
enter image source here
only the values to the left of #3# are included in
#color(white)("XXX")x < 3 # AND #x < 5#

In interval notation
#color(white)("XXX")in# means "in" or that #x# is included in the interval that follows;

#color(white)("XXX")#rounded brackets mean that the value beside the bracket is not included in the set (but everything up to that value) is;

#color(white)("XXX")#square brackets mean that the value beside the bracket is included in the set (as well as everything up to that value.

Note that the "infinite" values, #-oo# and #+oo# are always not included (always written with round brackets).

Some examples:
#color(white)("XXX")x in [-2,+7)# would mean #-2 <= x < 7#

#color(white)("XXX")x in (4,+oo)# would mean #4 < x# (with no upper limit)

For the given case
#color(white)("XXX")x < 3# implies #x < 5#
#color(white)("XXX")#so if both are included in th4e restrictions (AND) then only the #x < 3# is required
so we would write the interval as:
#color(white)("XXX")x in (-oo,3)#