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anonymous

  • one year ago

Help for a medal, anyone? I'm rusty on inequalities and need some help on a few problems to boost my memory. Here's the first one... -9 < 4x + 8 < 10

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  1. amistre64
    • one year ago
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    what are your thoughts ...

  2. anonymous
    • one year ago
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    If I remember correctly, you're supposed to simplify the equation by adding, divining..etc terms on either side, but I'm not sure how to do that with an inequality.

  3. anonymous
    • one year ago
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    dividing*

  4. amistre64
    • one year ago
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    the math doesnt change ... what you do to one part, you do to all the parts to keep them "equal" right?

  5. amistre64
    • one year ago
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    in this case, the equation is in the middle instead of to the left or right ... what would you think we should do first?

  6. amistre64
    • one year ago
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    just make a guess at what you think we should do to start with ... what comes to mind? 4x+8 is what we want to manipulate, how do we work about getting 'x' all by itself?

  7. anonymous
    • one year ago
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    Would you solve one equality at a time like -9 < 4x + 8 or 4x + 8 < 10 ?

  8. amistre64
    • one year ago
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    you can if you want, but i just work it all at once to avoid the extra work of writing it all out twice

  9. amistre64
    • one year ago
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    -9 < 4x + 8 < 10 -8 -8 -8 ---------------- -17< 4x < 2

  10. anonymous
    • one year ago
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    Ah, I see. Then you would divide all 3 parts by 4 to get x by itself.

  11. amistre64
    • one year ago
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    correct, the only thing to watch out for is when we have to mulitply or divide by a negative number ... which they really should include the rule when doing equalities the sign reverses ... but we do not have to worry about that in this particular case do we

  12. amistre64
    • one year ago
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    if -a < b, then a > -b if -a > b, then a < -b if -a = b, then a = -b ... the reversing of an equals sign just produces an equals sign, but it helps to make the rule consistent for all 3 equality signs.

  13. anonymous
    • one year ago
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    So would -17/4 < x < 1/2 be the final answer or is there another step?

  14. amistre64
    • one year ago
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    thats the answer for me, but im not grading it

  15. amistre64
    • one year ago
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    17/4 cant be reduced, but it can be written as 4 and 1/4 if need be

  16. anonymous
    • one year ago
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    Okay, thank you. :) Could you help with one other? It looks a bit different from the first.

  17. amistre64
    • one year ago
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    i spose

  18. anonymous
    • one year ago
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    \[\left|\frac{ x+4 }{ 5 } \right| < 6\]

  19. amistre64
    • one year ago
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    absolute value, what does that mean to you?

  20. anonymous
    • one year ago
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    I know that nothing inside of it can be negative (or at least that I recall)

  21. amistre64
    • one year ago
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    first off |5| = 5 so we can go ahead and multiply thru by 5 |x+4| < 30

  22. amistre64
    • one year ago
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    it can be negative inside of it, but the bars cancel out the sign

  23. amistre64
    • one year ago
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    |-30| = 30 and |30| = 30 when does x+4 = 30? or -30?

  24. amistre64
    • one year ago
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    as a side note: |a| < k can be written as: -k < a < k

  25. amistre64
    • one year ago
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    |x+4| < 30 can be written as -30 < x+4 < 30

  26. anonymous
    • one year ago
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    Then you just subtract 4 from both sides... -34 < x < 26 Also does the |a| < k or -k < a < k rule always apply?

  27. amistre64
    • one year ago
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    it is a rule, so it always applies yes. its just my brain that doesnt always remember it in time lol

  28. amistre64
    • one year ago
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    \[|\frac{x+4}{5}|<6\] \[-6<\frac{x+4}{5}<6\] \[-306<x+4<30\]

  29. amistre64
    • one year ago
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    not -306, but yeah

  30. anonymous
    • one year ago
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    Oh, okay. So -34 < x < 26 would be the answer correct?

  31. amistre64
    • one year ago
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    looks good to me

  32. anonymous
    • one year ago
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    Thank you so much for your help. :)

  33. amistre64
    • one year ago
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    youre welcome, and good luck :)

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