Question

-5 < 2y - 3 < 23


x - 4 < 5 or x + 2 > 15


5x - 4 > 6 or -4x + 5 > 1


inequalities

Answer 1

What's stopping you?

Add 3
Divide by 2
Read

Answer 2

ok, but what about for the other ones...im confused. I dont do well with questions like these. Im better off with multifple choice, so i can try to see what answers fits...

Answer 3

i dont even understand where to add the three and divide by 2..
:( sorry im so bad at this

Answer 4

First - "I dont do well with questions like these" Never say or think that again.
Second - What other ones? You must do them all simultaneously or you will wander off.

-5 < 2y - 3 < 23

Add 3

-5 + 3 < 2y - 3 + 3 < 23 + 3
Simplify
-2 < 2y < 26

Divide by 2...Your turn.

Answer 5

so i divide the 2 with the 2y and the negative 2 along with the 26

the -2 and the 2y cancle out which leaves y<13?

Answer 6

i find the horizontal format to be a little disorientating; which is why i go with the vertical format

-5 < 2y - 3 < 23
+3 +3 +3
---------------
-2 < 2y +0 < 26

Answer 7

Why do you want to discard one of the inequalities?
There is no such thing as "cancel out".

-2 < 2y < 26
Divide by 2

-2/2 < 2y/2 < 26/2
Simplify
-1 < y < 13

No "cancel"ing. Just division.

Answer 8

alright. hang on a second

Answer 9

now how would that look on a number line?

Answer 10

just find the -1 and 13, circle them to indicate that they are NOT included, and shade the solution set between the 2 numbers.

<---0=========0---->
-1 13

Answer 11

ohhhhhhhhh. ok :) thankyou!. do u mind helping me with the last two questions...i could really use the help...

Answer 12

ill check your ideas for solutions :)

whats your best idea for a solution to this one, or how would you suggest we go about it?

x - 4 < 5 or x + 2 > 15

Answer 13

well first, why does it say "or" between them?

Answer 14

or means that either solution set we get will work fine; just focus on the number parts at the moment

Answer 15

well would I add 4 to each side?

Answer 16

Notice how these CANNOT be put together like the first one. You must do them in two pieces. This is more clear from that number line. If you're dealing with the middle, you can join them. If they can't be joined, it must be the outside pieces.

Answer 17

lets try it

x - 4 < 5 or x + 2 > 15
+4 +4
---------
x + 0 < 9

that works for that part; what about the other part?

Answer 18

i would subtract 2 from each side?

Answer 19

good

x - 4 < 5 or x + 2 > 15
+4 +4 -2 -2
--------- ----------
x + 0 < 9 x + 0 > 13


so our solution set is:

x < 9 OR x > 13

Answer 20

wow, thankyou for that one. you are better than my instructor!! lol

Answer 21

Please demonstrate what that would look like on a number line.

Answer 22

well i think the 9 would have a circle with an arrow pointing < that way and the 13 would have a cirlce with the arrow pointing the other way

Answer 23

correct

<=====0-------0=====>
9 13

Answer 24

wow, see im getting the hang of it lol.
now off to the last one finally

Answer 25

the last one is very much like this one, except i see we have a division to watch out for

Answer 26

Why arent any of you teachers? sometimes I find people on here that help me better than my teacher does! yall are so smart

Answer 27

alot of us are getting math degrees to become teachers

Answer 28

5x - 4 > 6 or -4x + 5 > 1

what is our first steps for a solution set?

Answer 29

..or, if you don't like division by negative numbers, don't do it.

-4x + 5 > 1
Add 4x

5 > 1 + 4x

That way, you don't have to remember to "reverse the inequality". The addition does it for you!

Answer 30

are you? thats really cool!
ok back on subject, sorry I have ADD and I tend to go off into another world lol

Answer 31

that would be a suitable alternative, but if you cant recall to flip the sign; you prolly wont recall to swap the term

Answer 32

5x - 4 > 6 or -4x + 5 > 1

add or subtract first is always a good step, but what to add or subtract?

Answer 33

However, it is likely that you will remember addition. :-)

Answer 34

subtract 5 and then on the other one you want to add 4?

Answer 35

lets try it

5x - 4 > 6 or -4x + 5 > 1
+4 +4 -5 -5
--------- ----------
5x > 10 -4x > -4

nice, then?

Answer 36

great! so then you would divide by 5 and divide by -4?

Answer 37

so the first one would be x>2 and ten other would would be x>0?

Answer 38

good

5x > 10 -4x > -4
/5 /5 /-4 /-4
--------- ---------
x > 2 x ?? 1
^
something happens here

Answer 39

would the be <= ?

Answer 40

no = part; just a flip :)

Answer 41

so, our solution set is:

x < 10 OR x<1

Answer 42

thankyou so much.
so on the number line that would be a cirlce around 10 and a cirlce around the 1?

Answer 43

pfft, i cant read

x >2 OR x<1

Answer 44

circle the 1 and 2 yes

Answer 45

hahaha, its ok! i totaly messed up there too! lol gosh thankyou so much...If we were in person id give you the biggest hug! hahaha . you are the only one who actually took the time to help me!

Answer 46

and last step is we shade in the parts that are less than 1 OR greater than 2

<====0--------0=====>
1 2

Answer 47

youre welcome, thanks for learning :)

Answer 48

You made it well worth it!