Question 642506: Write the union of the intervals as a single interval
(-3, 2)⋃[1, 4)
Found 2 solutions by Century, Edwin McCravy:
Answer by Century(7)   (Show Source):
You can put this solution on YOUR website! Write the union of the union as a single interval
(-3, 2)U[1, 4)
The interval (-3,2) includes all the numbers from -3 to 2 not including either number.
The interval [1,4) includes all the numbers from 1 to 4 including 1 but not including 4.
Therefore to write the union which is the joining of the two pieces as a single interval we can write (-3,4).
Answer by Edwin McCravy(20065)  (Show Source):
You can put this solution on YOUR website!
(-3, 2)⋃[1, 4)
Put (-3,2) on a number line:
---------⚪==================⚪----------------
-5 -4 -3 -2 -1 0 1 2 3 4 5 6
Put [1,4) on a number line the same size:
-------------------------⚫===========⚪--------
-5 -4 -3 -2 -1 0 1 2 3 4 5 6
Write one number line under the other:
---------⚪==================⚪----------------
-5 -4 -3 -2 -1 0 1 2 3 4 5 6
-------------------------⚫===========⚪--------
-5 -4 -3 -2 -1 0 1 2 3 4 5 6
Now since it's ⋃ and not ⋂,
the graph of the answer is gotten by shading all that parts
that is shaded on ONE GRAPH OR THE OTHER,
So the graph is
---------⚪===========================⚪-------
-5 -4 -3 -2 -1 0 1 2 3 4 5 6
which in interval notation is (-3,4)
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By the way, if the problem had been
(-3, 2)⋂[1, 4) instead
we would have gotten to this step as above:
---------⚪==================⚪----------------
-5 -4 -3 -2 -1 0 1 2 3 4 5 6
-------------------------⚫===========⚪-------
-5 -4 -3 -2 -1 0 1 2 3 4 5 6
but then the graph of the answer would have been gotten
by shading ONLY that part that is shaded on BOTH graphs:
-------------------------⚫==⚪----------------
-5 -4 -3 -2 -1 0 1 2 3 4 5 6
and the answer in interval notation would have been [1,2).
You will no doubt have problems like that too.
Edwin
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