A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • 5 years ago

7w-3 ------ +3<5 2 how can I find the solution set?

  • This Question is Closed
  1. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[\left|7w-3 \right|\]

  2. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    The 7w-3 is an absoulte value

  3. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Well, start by moving the 3, to the other side and clearing the fractional part.

  4. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    3+7w-3=5 right?

  5. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    3+7w-3<5 I mean

  6. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    No. \[\frac{|7w-3|}{2} + 3 < 5\] \[\implies \frac{|7w-3|}{2} < 5 -3\] \[\implies |7w-3|< 2(5 + 3)\] Right?

  7. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Ack!

  8. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Should be \[|7w -3| < 2(5-3)\]

  9. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    7w-3<22

  10. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Did you get 7w<22/3?

  11. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    No.

  12. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    2*2 = 4.

  13. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    That means that 7w is less than 4 units away from 3.

  14. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    The part of the equation where you have 7w-3<2(5+3) =7w-3<10+6

  15. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I corrected that. It should be 2(5-3)

  16. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Not 2(5+3)

  17. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    So that means -4 < 7w - 3 < 4

  18. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Your right. And from there 7w<4-3 =7w<1 =w<1/7?

  19. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    No.

  20. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[|7w - 3| < 4 \]\[\implies -4 < 7w -3 < 4\]

  21. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Then you add 3 to each part of the relation.

  22. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[-4 + 3 < 7w - 3 + 3 < 4 + 3\]

  23. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Wow thats alot

  24. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Think about it. If I tell you that | x | < 1, That means that x is somewhere between 1 and -1.

  25. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Right?

  26. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    right

  27. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    So if I tell you that |x + 3| < 4, that means that x+3 is somewhere between -4 and 4

  28. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    So now we simplify and we have: \[-1 < 7w < 7\]

  29. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok, so I thought when we were at the 7w-3<4, we were almost finished. But we have to bring the 4 to the other side also and do it again.

  30. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    well you can work the two relations at the same time.

  31. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Dividing the whole thing by 7 we get...?

  32. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    1/7<w

  33. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    -1/7 is part of it. what's the other part?

  34. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    -1/7<w<7/7

  35. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Right.

  36. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    7/7=1

  37. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    -1/7<w<1 So would it be accurate that the solution set would become (-1/7, 1)?

  38. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    So w can be anything between -1/7 and 1 and the original relation \[\frac{|7w -3|}{2}+3 < 5\] Will be true.

  39. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Yep. (-1/7,1) is the solution set.

  40. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok, great. I understand now. Thanks for your help.

  41. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Just remember when you take off the absolute values that you have 2 possible solutions. \[|x| = a \implies x \in \{a,-a\}\] \[|x| < a \implies -a < x < a \] \[|x| \le a \implies -a \le x \le a \] \[|x| \ge a \implies x \le -a \ or\ a\le x \]

  42. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    etc.

  43. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Would the technique be the same if the absolute value contained a fraction? -2\[-2\left| 7-v/8 \right|+3-11?\] First step move the 8 over?

  44. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[2\left| 7-v/8 \right|\]

  45. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[-2\left| 7-v/8 \right|-3\]

  46. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    hello?

  47. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Sorry, was cleaning

  48. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Yes, it'd be the same technique move everything that's not inside the absolute value to the other side, then evaluate the absolute value by splitting it up into parts.

  49. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.