How do you solve and write the following in interval notation: # x <2# OR #x > 1#?

1 Answer
May 2, 2017

Answer:

#x<2" "OR" "x>1hArr(-oo,oo)#

Explanation:

#x<2# means #x# can take any value less than two and interval notation, this means #(-oo,2)#, meaning that all numbers between #-oo# and #1# are included and as #-oo# and #2# are not included we have use small brackets. This forms one set of numbers, say #P#.

#x>1# means #x# can take any value greater than one and interval notation tis means #(1,oo)# , meaning that all numbers between #1# and #oo# are included, but not #13# and #oo#. This forms another set of numbers, say #Q#.

Hence #x<2" "OR" "x>1# represents the union of two sets #P# and #Q# i.e #PuuQ# or in other words #(-oo,2)uu(1,oo)#.

Observe that #PuuQ# includes all the numbers from #-oo# to #oo# and hence #x<2" "OR" "x>1hArr(-oo,oo)#