Question

In a certain town the temperature, x in degrees Celsius on a certain day is described by two statements:

1.If 3 times the temperature is increased by 2, the temperature is still less than 14°C.
2.Twice the temperature minus 7 is greater than -11°C.



Part A: Create a compound inequality to represent the temperature range.

Part B: Can the temperature in this town be 5°C? Justify your answer by solving the inequalities in Part A

Answer 1

Part C: The average temperature in another town is 3°C, but the actual temperature is within 4°C of the average. Write and solve an inequality to find the range of temperature in this town.

Answer 2

Hey Kayla :)

The temperature is denoted by the variable x.
So for statement 1: `If 3 times x is increased by 2, then it is still less than 14°C.`

Here is how we would write that algebraically: \(\large\rm 3x+2\lt14\)
Do you understand what I did there?

We need to do a less than for the 2nd statement.

Answer 3

I mean a greater than*

Answer 4

maybe something like.. 2x - 7> 11

Answer 5

Ok very close! :)
The temperature is above -11, not 11.

Answer 6

oh ok yeah

Answer 7

Ummm so I guess for part A, they want us to isolate x in each inequality.
This will give us our temperature range.

Answer 8

\[\large\rm 3x+2\lt14\]Understand how to get x alone in this equation?
I would start by subtracting 2 from each side.

Answer 9

yeah 12 then divide by 3? so 4

Answer 10

Ok great, that gives us the first part of our compound inequality: \(\large\rm x\lt4\)

Answer 11

2x - 7> -11
+7 +7

2x > -4
-- --
2 2

x > -2

Answer 12

\(\large\rm x\gt-2\text{ and }x\lt4\)
Ok great! :)
That answers part A.

Answer 13

soo Part b is a no

Answer 14

bc x < 4 so it cant be 5

Answer 15

Ooo I think I made a boo boo.
Notice that in Part B it says:
`Justify your answer by solving the inequalities in Part A`

So for Part A, I guess they didn't want us to solve them... they wanted us to do that work in Part B.

So I suppose for Part A they actually wanted:
\(\large\rm 3x+2\lt14\text{ and } 2x-7\gt-11\)
Kinda weird :P

Answer 16

ok thats fine

Answer 17

So for Part B, you said no, and justified that by showing your work solving for x in each case. Good good good.

Hmm let's see what's going on with C here..

Answer 18

Mmm how to word this properly :d hmm let's see..

So our average temperature in another town is 3.
The actual temperature, x, can fluctuate up 4 degrees or down 4 degrees.

So our temperature x can be as high as 3+4,
and as low as 3-4,
ya?

Answer 19

yeah so between -1 and 7

Answer 20

Good good good! :)
So if you need to first write the inequality before you solve, I would probably do it like this:
Say that \(\large\rm x\lt 3+4\text{ and }x\gt 3-4\)
Which leads to your compound inequality again: \(\large\rm x\lt7\text{ and }x\gt-1\)
If we wanted to, we could write it like this: \(\large\rm -1\lt x\lt7\)

Yayyy good job Kayla \c:/

Answer 21

Yay! Thank you sooooo much for your time and help!

Answer 22

np \c:/