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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

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  1. anonymous
    • one year ago
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    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
    • one year ago
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    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
    • one year ago
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    I mean a greater than*

  4. anonymous
    • one year ago
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    maybe something like.. 2x - 7> 11

  5. zepdrix
    • one year ago
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    Ok very close! :) The temperature is above -11, not 11.

  6. anonymous
    • one year ago
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    oh ok yeah

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

  9. anonymous
    • one year ago
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    yeah 12 then divide by 3? so 4

  10. zepdrix
    • one year ago
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    Ok great, that gives us the first part of our compound inequality: \(\large\rm x\lt4\)

  11. anonymous
    • one year ago
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    2x - 7> -11 +7 +7 2x > -4 -- -- 2 2 x > -2

  12. zepdrix
    • one year ago
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    \(\large\rm x\gt-2\text{ and }x\lt4\) Ok great! :) That answers part A.

  13. anonymous
    • one year ago
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    soo Part b is a no

  14. anonymous
    • one year ago
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    bc x < 4 so it cant be 5

  15. zepdrix
    • one year ago
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    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
    • one year ago
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    ok thats fine

  17. zepdrix
    • one year ago
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    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
    • one year ago
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    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
    • one year ago
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    yeah so between -1 and 7

  20. zepdrix
    • one year ago
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    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
    • one year ago
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    Yay! Thank you sooooo much for your time and help!

  22. zepdrix
    • one year ago
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    np \c:/

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