anonymous
  • 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
Algebra
katieb
  • katieb
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anonymous
  • 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
  • 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
  • zepdrix
I mean a greater than*

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anonymous
  • anonymous
maybe something like.. 2x - 7> 11
zepdrix
  • zepdrix
Ok very close! :) The temperature is above -11, not 11.
anonymous
  • anonymous
oh ok yeah
zepdrix
  • 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
  • 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
  • anonymous
yeah 12 then divide by 3? so 4
zepdrix
  • zepdrix
Ok great, that gives us the first part of our compound inequality: \(\large\rm x\lt4\)
anonymous
  • anonymous
2x - 7> -11 +7 +7 2x > -4 -- -- 2 2 x > -2
zepdrix
  • zepdrix
\(\large\rm x\gt-2\text{ and }x\lt4\) Ok great! :) That answers part A.
anonymous
  • anonymous
soo Part b is a no
anonymous
  • anonymous
bc x < 4 so it cant be 5
zepdrix
  • 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
  • anonymous
ok thats fine
zepdrix
  • 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
  • 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
  • anonymous
yeah so between -1 and 7
zepdrix
  • 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
  • anonymous
Yay! Thank you sooooo much for your time and help!
zepdrix
  • zepdrix
np \c:/

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