Please help me with writing inequalities for intervals and graphing them.
Ex:
[ -4,5]
( ∞, -1] or (3,∞)
Can someone teach me how on these two problems. Thanks in advance.

- anonymous

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- phi

how much do you know?

- anonymous

not a lot

- phi

[-4,5]
means from-4 to +5

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## More answers

- anonymous

oh okay so far that helped me tons

- phi

to "graph" it, show a number line, and draw a line to show the numbers from -4 to +5
can you do that ?

- anonymous

i think so

- anonymous

i'm trying right now

- anonymous

okay I did it

- phi

the [ in [-4,5] means -4 is part of the answer
to show that, put a solid dot at -4
ditto for the +5

- anonymous

okay done

- phi

|dw:1444425810562:dw|

- anonymous

ooh yay! thank you

- phi

for inequalities
people use "x" for the number
you want x "between" -4 and 5
you want x bigger than (or equal) to -4
and you want x less than or equal to +5

- anonymous

so im going to use the less than or equal to sign when I write the inequality sign correct?

- anonymous

-4 is less than or equal to x5?

- phi

I would write it as -4 is less than or equal to x and x is less than or equal to 5

- anonymous

thank you so so much

- anonymous

for the next question does the ∞ in the problem mean that is goes on. meaning that it has no ending?

- phi

you put the small point end of < or \(\le\) next to the smaller side, and the big fat side next to the bigger number

- phi

infinity is not a number, it is more like an idea: "keep going"
I assume you left out an minus sign and mean
( - ∞, -1] or (3,∞)

- anonymous

yes sorry

- phi

(- infinity, -1]
to graph, put a solid dot at -1 (solid because of the ] )
and draw a solid line in the direction of more negative numbers. put an arrow on it to show it "keeps going"

- phi

on the same graph put
(3,∞)
the ( 3 means it starts at 3 and ∞) means all numbers after 3
the ( part means 3 is not part of the graph, i.e. all numbers bigger than 3 but not including 3. Use an OPEN circle at 3 instead of a solid dot.

- anonymous

okay so |dw:1444426396931:dw|

- phi

yes, that is the first part

- anonymous

okay then |dw:1444426668016:dw|

- phi

yes.
as inequalities it is
\[ x \le -1 \cup x > 3 \]

- anonymous

thank you so much phi

- anonymous

is that all?

- phi

yw

- anonymous

have a nice night

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