Question

Can anyone help me?

Solve the compound inequality.
2w+5<7 and 3w-6>= 12

Check out the image below...

Answer 1

@Missiey Can you help with this one?

Answer 2

give me a sec

Answer 3

for this one
2w+5<7
add -5 to both sides. can you do that?

Answer 4

2w+5 <7
-5 -5
-----------
2w < 2

Correct?

Answer 5

yes. now divide both sides by 2

Answer 6

2w < 2
/2 < /2
--------
w < 1

Answer 7

yes. that means w is smaller than 1 (notice the "small end" of the < is next to the w)
so the answer is (so far)
, 1)
we need to find what w is bigger than

Answer 8

3w-6>= 12

any ideas? what is a good thing to add to both sides?

Answer 9

3w - 6 >= 12
+6 >= +6
---------------
3w >= 18
/3 >= /3
------------
w >= 6

Correct?

Answer 10

yes. that means w is equal to or bigger than 6
so we have
w is smaller than 1 and at the same time 6 or bigger

guess what? there is no number that works.

Answer 11

So the answer is the zero with the / through it??

Answer 12

yes, the "null set" which is a fancy way to say, no solution

Answer 13

Thanks! Could you help me with a few more? Just to make sure i'm doing them right?

Answer 14

4x - 5 <= 11
and
3x - 4 <= - 16

Answer 15

4x - 5 <= 11
+5 <= + 5
---------------
4x <= 16
/4 <= /4
-----------
x <= 4

Answer 16

@Alireem94 you are in good hands I am going to jump on aleks and get some work done..here if u need

Answer 17

3x - 4 <= -16
+4 <= +4
---------------
3x <= -12
/3 <= /3
--------------
x <= -4

Answer 18

yes. so you have x<=4 and at the same time x<= -4
both have to be true at the same time. what do you think?

Answer 19

I really have no idea how to determine this part

Answer 20

The first idea is you can simplify the conditions
if you have to be less than or equal to -4, then saying oh and we want to be less than 4 is a useless thing to add. Do you agree?

Answer 21

Yes

Answer 22

so x<=-4 and x<=4 simplifies to x<= -4

what is the biggest x can be ?

Answer 23

4?

Answer 24

\[ x \le -4\]
what is the biggest x can be ?

Answer 25

-4

Answer 26

is x allowed to be -4 ?

Answer 27

yes, that is what the \( \le \) means. If it were just <, then x would not be

Answer 28

Oh ok... So x is less than OR equal to -4

Answer 29

now we can fill in the answer

we want
( or [ smallest , biggest ) or ]
we use ] for \( \le\) and we use ) for <

Answer 30

we know the biggest number x can be, -4
and it can equal -4, so we use ]

so we have
, -4]
now what is the smallest x can be ?

Answer 31

x<= -4
has no restriction on how negative x can be. -1000, -100000, ....
so we say x can be -infinity= \( - \infty\)
for infinity, we always use the ( and never [ as the bracket
because infinity is not a number, it is more like an "idea":

Answer 32

So it's (−∞, -4]

Answer 33

yes

Answer 34

Thank you!!!