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Lineêre ongelykhede

Ondersoek : ongelykhede op 'n getallelyn

Stel die volgende voor op getallelyne:

  1. x = 4
  2. x < 4
  3. x 4
  4. x 4
  5. x > 4

'n Lineêre ongelykheid is soortgelyk aan 'n lineêre vergelyking aangesien die hoogste eksponent van die veranderlike 1 is. Die volgende is voorbeelde van lineêre ongelykhede:

2 x + 2 1 2 - x 3 x + 1 2 4 3 x - 6 < 7 x + 2

Die metodes wat gebruik word om lineêre ongelykhede op te los, is identies aan dié wat gebruik word om lineêre vergelykings op te los. Die enigste verskil kom voor wanneer daar 'n vermenigvuldiging met of deling deur 'n negatiewe getal is. Ons weet byvoorbeeld dat 8 > 6 . As beide kante van die ongelykheid gedeel word (byvoorbeeld deur - 2 ), sien ons - 4 is nie groter as - 3 nie. Dus moet die ongelykheid omkeer, wat beteken - 4 < - 3 .

Wanneer beide kante van 'n ongelykheid met 'n negatiewe getal vermenigvuldig word, of met 'n negatiewe getal gedeel word, verander die rigting van die ongelykheid. Om hierdie rede mag ons nie met 'n veranderlike vermenigvuldig as ons nie weet nie wat die onbekende (veranderlike) se teken is nie.

Byvoorbeeld, as x < 1 , dan - x > - 1 .

Om 'n ongelykheid met 'n gewone vergelyking te vergelyk, sal ons eers die gewone vergelyking oplos. Los op 2 x + 2 = 1 .

2 x + 2 = 1 2 x = 1 - 2 2 x = - 1 x = - 1 2

As ons hierdie antwoord op 'n getallelyn voorstel, kry ons:

Kom ons los nou die ongelykheid 2 x + 2 1 op:

2 x + 2 1 2 x 1 - 2 2 x - 1 x - 1 2

As ons hierdie antwoord op 'n getallelyn voorstel, kry ons:

Soos jy kan sien, vir die vergelyking is daar slegs 'n enkele waarde van x waarvoor die vergelyking waar is. Vir die ongelykheid is daar egter 'n hele versameling waardes waarvoor die ongelykheid waar is. Dit is die groot verskil tussen gewone vergelykings (gelykhede) en ongelykhede.

Khan akademie video oor ongelykhede - 1

Khan akademie video oor ongelykhede - 2

Los op vir r : 6 - r > 2

  1. - r > 2 - 6 - r > - 4
  2. Wanneer jy met 'n negatiewe getal vermenigvuldig, draai die rigting van die ongelykheid om.

    r < 4

Los op vir q : 4 q + 3 < 2 ( q + 3 ) en stel die oplossing voor op 'n getallelyn.

  1. 4 q + 3 < 2 ( q + 3 ) 4 q + 3 < 2 q + 6
  2. 4 q + 3 < 2 q + 6 4 q - 2 q < 6 - 3 2 q < 3
  3. 2 q < 3 deel beide kante deur 2 q < 3 2

Los op vir x : 5 x + 3 < 8 en stel die antwoord op 'n getallelyn voor.

  1. 5 - 3 x + 3 - 3 < 8 - 3 2 x < 5

Lineêre ongelykhede

  1. Los op vir x en stel die oplossing grafies voor:
    1. 3 x + 4 > 5 x + 8
    2. 3 ( x - 1 ) - 2 6 x + 4
    3. x - 7 3 > 2 x - 3 2
    4. - 4 ( x - 1 ) < x + 2
    5. 1 2 x + 1 3 ( x - 1 ) 5 6 x - 1 3
  2. Los die volgende ongelykhede op. Illustreer jou antwoord op 'n getallelyn as x 'n reële getal is.
    1. - 2 x - 1 < 3
    2. - 5 < 2 x - 3 7
  3. Los op vir x : 7 ( 3 x + 2 ) - 5 ( 2 x - 3 ) > 7 Illustreer die antwoord op 'n getallelyn.

Questions & Answers

Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
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please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
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industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
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How we are making nano material?
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scanning tunneling microscope
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what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
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if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
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analytical skills graphene is prepared to kill any type viruses .
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what is Nano technology ?
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write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
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what king of growth are you checking .?
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What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
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yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
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biomolecules are e building blocks of every organics and inorganic materials.
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Introduction about quantum dots in nanotechnology
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nano basically means 10^(-9). nanometer is a unit to measure length.
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Source:  OpenStax, Siyavula textbooks: wiskunde (graad 10) [caps]. OpenStax CNX. Aug 04, 2011 Download for free at http://cnx.org/content/col11328/1.4
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