## anonymous one year ago 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

1. 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.

2. 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.

3. zepdrix

I mean a greater than*

4. anonymous

maybe something like.. 2x - 7> 11

5. zepdrix

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

6. anonymous

oh ok yeah

7. zepdrix

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

8. zepdrix

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

9. anonymous

yeah 12 then divide by 3? so 4

10. zepdrix

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

11. anonymous

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

12. zepdrix

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

13. anonymous

soo Part b is a no

14. anonymous

bc x < 4 so it cant be 5

15. 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

16. anonymous

ok thats fine

17. 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..

18. 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?

19. anonymous

yeah so between -1 and 7

20. 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:/

21. anonymous

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

22. zepdrix

np \c:/