Quantcast

A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

timo86m

  • 3 years ago

It's been a while but what are the rules for sign flipping when solving inequalities For example I know when you multiply by a negative number you have to flip the sign as in -2x>4 x<-2 Notice that it flipped. What are the other rules for sign flipping?

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

    also if you divide by a negative number

  2. timo86m
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    what about the reciprocal how does that work?

  3. Syderitic
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    hum, it flips every time you multiply both sides of the equation by -1 ex -2x>4 <=> -4>2x ,rearrange and you get 2x<-4

  4. myininaya
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    5>4 But 1/5<1/4 So flip when doing reciprocal of both sides ---------- Also 5>-4 But -5<4 So flip also when multiplying(or dividing) both sides by a negative

  5. timo86m
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    can you give me a simple example involving a variable when you have to use the reciprocal?

  6. timo86m
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    oh i see thank @myininaya

  7. timo86m
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    what if it was -1/x<7

  8. timo86m
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    -x>1/7 x<-1/7 ?

  9. myininaya
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    oh wait @timo86m i made a mistake sorry

  10. Syderitic
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    okay, 4/x>1/3 =>(mult by x) 4x/x>x/3 => 4>x/3 (mult by 3) 3*4>3x/3 =>12>x , since x switched, you switch the equation getting x<12

  11. myininaya
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    \[\frac{1}{x}<7\] I made the assumption earlier that x>0 but I didn't tell you that so we can't just simply flip .... i will show you how to solve this

  12. myininaya
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    unless x is always greater 0

  13. myininaya
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    but like i said i didn't say that so the way to solve this one is...

  14. timo86m
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ah ok

  15. myininaya
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    \[\frac{1}{x}-7 <0\] \[\frac{1}{x}-\frac{7x}{x} <0\] \[\frac{1-7x}{x}<0\] The expression (1-7x)/x is zero when 1-7x=0 => x=1/7 The expression (1-7x)/x is undefined when x=0 So we do a number line and test the intervals around 0 and 1/7 ---|---|--- 0 1/7 Choose number in each of the three intervals -1 1/10 25 Ok So plug into expression \[\frac{1-7x}{x}\] For -1, we get (1-7(-1))/(-1)=8/(-1)=-8 But -8<0 This satisfies the inequality For 1/10, we get (1-7(1/10))/(1/10)=10(1-7(1/10))=10-7=3>0 But 3>0 This does not satisfy the inequality For 25, we get (1-7(25))/25=some negative number Which also satisfies the inequality So The intervals (-inf,0) U (1/7,inf) are the solution to the inequality

  16. myininaya
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Ok but @timo86m if x was always greater than 0 then we could have simply took reciprocal of both sides and flip the inequality sign

  17. myininaya
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Like I did before

  18. timo86m
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    we could just assume that and make it easier lol.

  19. myininaya
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    but if is doesn't say that x>0 then you cannot assume it lol but yes it would have made things none easier

  20. myininaya
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Ok let me give an example where you don't have to worry about being wrong when taking reciprocal ... one sec

  21. timo86m
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    well specify like x>0 and x>n

  22. myininaya
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    \[\frac{1}{e^x}<7 \] \[\frac{1}{e^x}-7<0\] \[\frac{1}{e^x}-\frac{7 e^x}{e^x}<0\] \[\frac{1-7e^x}{e^x}<0\] The expression on bottom is always greater than 0 so this expression is defined everywhere But 1-7e^x=0 when 1=7e^x => 1/7=e^x => ln(1/7)=x --------------|---------- ln(1/7) Test both intervals -2 0 So plug in -2 we get some positive number Plug in 0 we get 1-7=-6 <0 which satisfies the inequality So the solution is (ln(1/7),inf) But we could have did \[\frac{1}{e^x} <7\] \[e^x>\frac{1}{7}\] \[x>\ln(\frac{1}{7})\] much eaiser ! :) We can do this because e^x is always greater than 0

  23. timo86m
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    thanks :) Sorry i had to go suddenly family emergency came up :)

  24. 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.