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- anonymous

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

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- anonymous

- katieb

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- anonymous

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.

- zepdrix

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.

- zepdrix

I mean a greater than*

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- anonymous

maybe something like.. 2x - 7> 11

- zepdrix

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

- anonymous

oh ok yeah

- zepdrix

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

- zepdrix

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

- anonymous

yeah 12 then divide by 3? so 4

- zepdrix

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

- anonymous

2x - 7> -11
+7 +7
2x > -4
-- --
2 2
x > -2

- zepdrix

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

- anonymous

soo Part b is a no

- anonymous

bc x < 4 so it cant be 5

- zepdrix

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

- anonymous

ok thats fine

- zepdrix

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..

- zepdrix

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?

- anonymous

yeah so between -1 and 7

- zepdrix

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:/

- anonymous

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

- zepdrix

np \c:/

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