Question

The lesson is equations and inequalities in my intermediate algebra class. I didn't get much of an explanation and I'm supposed to graph a set and "write it as a single interval if possible." I'm still extremely unsure and I'm hoping for someone to help me with the following problem as an example: (-5, 2] U (-1, 3)

Answer 1

(-5, 2] is the interval from -5 to 2

the -5 is NOT included in the interval due to the parenthesis
the 2 is included because of the square bracket

Answer 2

what does (-1,3) mean in interval notation?

Answer 3

The -1 and 3 don't have to be included?

Answer 4

yes we're going from -1 to 3 (excluding both)

Answer 5

what I would do from here is draw out 3 number lines

line them up (so all the zeros line up vertically, all the ones line up vertically, etc etc)

Answer 6

for the first number line up at the very top, plot the graph for (-5, 2]

so you'll have an open circle at -5 to exclude -5
a closed circle at 2 to include 2
and then shade everything in between

Answer 7

let me know when you've done that

Answer 8

I did it.

Answer 9

now for the middle number line, plot the interval from -1 to -3

you'll have open circles at the endpoints

Answer 10

Okay.

Answer 11

Is that all I have to do?

Answer 12

oops typo, I meant to say "plot the interval from -1 to 3" (not -3, but positive 3)

but you get the idea

Answer 13

so you should have this so far (see attached)

Answer 14

for that last number line, you're going to combine the first two plots as one

basically you just merge the two plots straight down to get this picture

Answer 15

I basically cut/paste and moved things down

Answer 16

the combined interval runs from -5 to +3 excluding both endpoints due to the open circles

Answer 17

so (-5, 2] U (-1, 3) boils down to (-5,3)

Answer 18

this is only possible because we have that overlap on the last number line

if there is no overlap, then you can't reduce it down to a single interval

Answer 19

Okay, thank you.

Answer 20

you're welcome