Question

Please help! I have a complicated word problem.

Answer 1

In a certain town, the inches of rainfall, x, on a certain day is described by two statements:


If 3 times the rainfall is increased by 2, the rainfall is still less than 26 inches.
5 plus twice the rainfall is greater than 11 inches.


Part A: Create a compound inequality to represent the rainfall range. (3 points)

Part B: Can the rainfall in this town be 4 inches? Justify your answer by solving the inequalities in Part A. (3 points)

Part C: The average rainfall in another town is 5 inches but the actual rainfall is within 4 inches of the average. Write and solve an inequality to find the range of rainfall height in this town. (4 points)

Answer 2

We know that rainfall on that particular day is x inches.
Let's try to create inequality for the first statement:
If 3 times the rainfall is increased by 2, the rainfall is still less than 26 inches.
Can you try?

Answer 3

@micahpkay ???

Answer 4

Sorry about that. I accidentally exited my window with a bunch of tabs open and it took forever to load again.

Answer 5

3x + 2 < 26

Answer 6

yes, correct :)
now how about
5 plus twice the rainfall is greater than 11 inches.
?

Answer 7

2x + 5 > 11

Answer 8

But what do I do with these expressions?

Answer 9

good.
could you solve them ?

Answer 10

those are inequalities, you can isolate 'x' from each of them

Answer 11

*equations

Answer 12

3x + 2 - 2 < 26 - 2

3x < 24

3x/3 < 24/3

x < 8

Answer 13

2x + 5 > 11

2x + 5 - 5 > 11 - 5

2x > 6

2x/2 > 6/2

x > 3

Answer 14

Correct?

Answer 15

yes!
so x can take any value which is >3 and less than 8
so, can x take the value of 4 ?

Answer 16

Yes.

Answer 17

Would I write it as 3 < x < 8?

Answer 18

yes,

Answer 19

So is "3 < x < 8?" the answer to Part A?

Answer 20

yes, yes it is!

Answer 21

Sorry about leaving. Are you still there?

Answer 22

yes

Answer 23

Okay.

Answer 24

Can you help me on Part C?

Answer 25

actual rainfall is within 4 inches of the average (=5)
so, let the actual rainfall be 'x'

x is not more than 4 inches greater than 5
or
x is not less than 4 inches lesser than 5
can you try to make an equality ?

Answer 26

no... 5 is avg. and x can be only 4 inches far from 5

so,
x-4 < 5 or x+4 >5

Answer 27

So do I simplify these inequalities?

Answer 28

yes, and then you can prepare a compound inequality from it :)

Answer 29

x - 4 < 5

x - 4 + 4 < 5 + 4

x < 9

Answer 30

yes

Answer 31

x + 4 > 5

x + 4 - 4 > 5 - 4

x > 1

Answer 32

yes

Answer 33

So now what?

Answer 34

x> 9 or x<1
try to combine this ?

Answer 35

9 < x < 1

Answer 36

How is that even possible??

Answer 37

oh wait, its x<9
not x>9 that you found

so, combine
x<9 and x>1

Answer 38

Yeah. That's what I thought. lol

Answer 39

1 < x < 9

Answer 40

yes, it is :)

Answer 41

Okay thanks. :)

PS: I found x < 9, not x > 9.

Answer 42

yeah, yes.

Answer 43

The instructions say to write AND solve the inequality. How do I "solve" it?

Answer 44

you already solved it, solve means to isolate x
write the inequality : x-4 < 5 or x+4 >5
solve it : ..... 1 < x < 9

Answer 45

Oh, okay.

Answer 46

Thanks for helping me! You deserve 10 medals! lol

Answer 47

:)

Answer 48

you're most welcome ^_^
you understood it, thats my medal :)

Answer 49

How sweet. I'm crying. jk :)

Answer 50

It's 5:00 in the morning where I live. Time for bed. lol

Answer 51

ohh! have a good night and sweet dreams :)

Answer 52

You too. Cya!

Answer 53

Final Answer

Part A:

3x + 2 < 26

3x + 2 - 2 < 26 - 2

3x < 24

3x/3 < 24/3

x < 8
_____

2x + 5 > 11

2x + 5 - 5 > 11 - 5

2x > 6

2x/2 > 6/2

x > 3
_____

If "x" is greater than 3 but less than 8, I can write the compound inequality shown below.

3 < x < 8

Part B:

Yes, it can be 4 inches because 4 is greater than 3 and less than 8. I already solved the inequalities in Part A.

Part C:

x - 4 < 5 or x + 4 > 5
_________________________

x - 4 < 5

x - 4 + 4 < 5 + 4

x < 9
_____

x + 4 > 5

x + 4 - 4 > 5 - 4

x > 1
_____

Since "x" is greater than 1 but less than 9, I can write the compound inequality shown below.

1 < x < 9

Answer 54

seems good :)

Answer 55

Thanks.

Answer 56

Okay. I'm going to bed now for sure. Bye!

Answer 57

bye :) sleep tight.