Question

ONE Other Algebra I Question - Compound Inequalties?

Answer 1

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

If 3 times the air pressure is increased by 2, the pressure is still less than 92 inches.
Twice the air pressure minus 39 is greater than 11 inches.



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

Part B: Can the air pressure in this town be 24 inches? Justify your answer by solving the inequalities in Part A. (3 points)

Part C: The average air pressure in another town is 29 inches but the actual pressure is within 4 inches of the average. Write and solve an inequality to find the range of air pressure in this town. (4 points)

Answer 2

I think I might have Part A.
Statement I: 3x + 2 < 92
Statement II: 2x -39 > 11

But is this a conjunction or disjunction?

Answer 3

@DebbieG @savannaxx_

Answer 4

Well, it says that the air pressure adheres to these two conditions. So BOTH hold, therefore, BOTH of these are true.

Answer 5

And thank you for the testimonial - very appreciated. :)

Answer 6

So when BOTH of these are true - then that means that is is a conjunction because conjunctions joins the two inequality - am I correct?

Answer 7

Right - they must BOTH hold:

3x + 2 < 92 AND 2x -39 > 11

So when you solve the individual inequalities, you combine the solution sets by taking the INTERSECTION.

If you had and "OR" compound inequality, then you would combine by taking the UNION.

Answer 8

So that would make inequality 1 equal x < 30 and equation 2 equal x > 25. Since Part B is asking if the air pressure can be 24 inches...I think it can. because when graphing conjunctions you shade in between. So I am thinking that you can have an air pressure of 24 - am I correct?

Answer 9

Hmmmmm.... look at your solution set again.

You are correct that you get:

x > 25 AND x < 30

So does x = 24 satisfy those conditions? remember, it is an AND inequality, so it must satisfy BOTH conditions.

(you are correct, that in terms of graphing the solution set on a number line, you shade the part "in between" the two endpoints)

Answer 10

x is more than 25 and less than 30. X is the...inches...of...air pressure - OH! Goodness. So it won't satisfy to be 24 inches. Oops. Okay, so let me try to solve Part C.

Answer 11

I don't really get how it is asking me to make an inequality in Part C. 4 inches "of" 29? Is that multiplication?

Answer 12

No, within 4 inches of 29.

So, up to 4 inches greater, or 4 inches less, than 29.

Answer 13

So that means That means this is an injunction.
x < 29 - 4 or x > 29 - 4

Answer 14

nooo..... on a couple of counts.

first off, not an "or", it's an "and".

And second, that is not set up correctly! That would mean that: x<25 OR x>25. So really, x could be anything BUT 25! That does NOT insure that x is "within 4" of 29.

Look at it this way: If you are 29 years old, and I am WITHIN 4 years of your age (HAH I wish lol).... then what are the possibilities for my age?

I have to be AT LEAST 29 - 4 years old, so I am at least 25, so my age is \(\ge 25\)
And I have to be NO MORE THAN 29 + 4 years old, so I am NO MORE than 33, so my age is also \(\le 33\)

Only if BOTH of those conditions hold:
\(age \ge 25\) AND \(age \le 33\)

Answer 15

oops, entered too soon - only if they BOTH hold, am I WITHIN 4 years of your age.

Answer 16

So my age is "sandwiched" BETWEEN 25 and 33, right?

\(25\le age \le 33\)

Answer 17

Okay. Yeah. Sorry for the confusion.

Answer 18

Well, @DebbieG , that was it really. I am very grateful for you helping me in this. I watched videos and read the lessons and I thought I had it, but when these questions came to my eye, I knew I was confused. Thank you very much.

Answer 19

You're welcome, happy to help. :)