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In this video we are going to take a look at solving an inequality that is a compound in equality like you see here
right here and is in a table in a graphing calculator in the last video we had this graph and we
solved this same compound inequality using the graph and intersection feature in our calculators, now we are going to take our calculator and have
it do a table, notice that since we already have this in our calculator
we already have -2 in our y1 and we already have 2x-4 in our y2 and we already have 8 in our y3 we can go ahead and leave it like that
for the table or you can just compare values by looking at the y2 column in the table
now the first thing we need to do is set up our table in order to view the solutions to the compound inequality in the table to
do that we're going to push the green diamond button and above f4 notice that it says tbl set
so we need that
now on this it has tbl start that is where we want to start and we are not quite sure where the solutions are so we need to start at a value that
is low enough that we will probably get our solution how about if we go ahead and start at -5
so we are going to do -5 and make sure that you use a negative symbol to enter that if you use a minus it will give you an error
and notice right below that there is this little triangle infront of tbl which is
short for table, the little triangle is a symbol we use in math for change in table
well this is change and the tbl after makes it mean change in table
now right now it has so it is changing so that in between each value in our table will have it go up by 1 if you need something a little
more accurate you can have it jump by 1/2 by putting in .5 or 1/10 by putting .1, it depends on how accurate
your problem wants you to be, jumping by 1s is probably going to be fine for us, not you need to hit enter twice
and when you go to your table which will be the green diamond button and table you will see all the values for your
y1s, y2s, and y3s, notice y1 is always -2 because that is what we told it to be
y3 is always 8 because that is what we told it to be
so what we need to do is basically just arrow down in our calculator and find when this middle column
which is the y2s and also representing this 2x-4
is greater than or equal to -2 and less than or equal to 8, now to do that right now
the values are smaller than -2 so we are going to arrow down until we reach
a value of -2 in the y2 column and compare what happens before it and what happens after
so we are going to use our arrow key and notice it is arrowing down the x values
and we are going to watch until we get to -2 and notice right here
where the x = 1 we got to the spot where the y2 = -2 and it also matches our y1 column
we need to compare what happens right before it and what happens right after because we want y2 to be larger than
y1 or y2 to be larger than -2
If you look at just before when x is 0 the y2 is -4 which is smaller
If you look just after the y2 is 0 which is larger, so it looks like we have this situation right here from our inequality from 1 forward.
We can actually start our interval notation
by using a square bracket since our inequality has a line under it and 1
and 1 as our first value then a comma. Now we need to continue on through our table to find out when
this y2 hits the 8 because that is going to be our next spot where we need to examine. So if you arrow down farther
and you watch notice all of a sudden y2 is 8 so we are going to go one more so we can take a look at what happens just before and what
happens just after. Notice at 6 the y2 is 8 if we
look at just before it the y2 is 6 and 6 is smaller than 8 and in this statement here we want
this 2x-4 which is our y2 to be less than or equal to 8, well just before 6 it is less than 8
and right at 6 it is 8 which is what this line under neath the inequality is wanting
if you examine just after 6 on your table notice that the y2 is 10
and 10 and larger than 8, so when you go past 6 we no longer have this situation here being satisfied.
So 6 is your turning point and we want everything before 6. Which means
in our
notation here we want to put a 6 in our ending spot and since we have a line under our inequality we use a square bracket.
This is saying that the x values that satisfy this compound inequality are when
are when x is greater than or equal to 1 and less than or equal to 6. Which is what we found in our table.
Our interval notation looks like this and notice that this is the same we got when we solved by graphing. Our set notation is going to require
us to take this statement right here and put a straight line for such that in front of it
and then a x
and then the
set brackets
around this
statement and we read this as the set of all x such that 1 is less than or equal to x which is less than or equal to 6
and that is how you would solve using a table in the TI 89
Now let's take a look at a Casio.
notice that in the Casio because we did this same problem by graphing we have all our values in the
y1, y2, y3, and we still have our graph here
once we have all that taken care of we want to go to this button right here that looks like it has little tables next to the y1,
y2 button if you press that
notice that this table shows up here. If you want to view the table larger than it currently is you can go down to this button right here that says
resize and that makes it much easier to view a table, now notice that on this table we only get 3 columns
if you use the scroll bar here you can move back and forth
across. Notice I can scroll over and see y2 and y3 and the x stays the same over here. Now I am currently just concerned about y1 and y2
in order to take care of this part of the inequality
once we are done with that part we will use the scroll bar to scroll over and compare y2 with y3
now
we need to set this table so it is doing everything correctly. Right now it is jumping by .5 which is fine; however, if we want to make it
look like the one that we did in the TI, we use this button right here with the two arrows and the x and y
click on that and it will ask where you want the table to start
and starting at -2 is fine, if we want it to match what we had in the TI we can punch in -5
and it also asks where you want it to end, well we are not quite sure where we want it to end but we want it to
keep going for a while so how about if we have it go up to 10
and then the step is how far it is going to be from one entry in the table to the next entry right now it is jumping by
.5 to make it look like the TI we will just press in 1 and then click OK
now if you look at it notice that the x values go up by 1 and it starts at -5 and if we
scroll down using the scroll bar here it goes all the way to 10
so let's take a look at the column and glance down and find where the y1 and the y2 match and they match right here when x = 1
again if you look just before that you will notice that at x = 0 we have a
y1 = -2 and a y2 = -4
-4 is smaller and we want -4 to be larger because we need the y2 here to be larger than the y1
so before where x = 1 is not going to work so let's look just after
at 2 and if you look at the 2 here the y2 is 0 and the y1 is -2 and 0 is
larger so after this spot where x = 1 seems to work
for statement where we want out y1 to be smaller than y2
so that again gives us this first part of our inequality
now we need the second part of our solution over here and for that we need to compare our y2 to y3 so if you just scroll over
and then continue down
you will notice right here at 6 they match
so if you compare right before that the y2 is 6 and the y3 is 8 and 6
is smaller than 8 which is what we want in our solution here we want the y2 to be smaller than the y3
if you look just after here you will notice when x is 7 y2 is 10 and y3 is 8 well 10
is bigger we don't want y2 to be bigger so the things after 6 are not part of our solution
that means that we need to finish off our inequality the same way we did here for the TI
so that is how you use your table function in the Casio and we write our solution over here the same way we did her for the TI