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Wiskunde

Graad 8

Heelgetalle, vergelykings en meetkunde

Module 7

Vergelykings

Die “wonderwêreld” rondom VERGELYKINGS

KLASOPDRAG 1

  • Kom ontdek stap vir stap meer omtrent ... wat is ’n vergelyking, en hoe om dit op te los.

1. Wat verstaan jy onder die term: “vergelyking” ?

2. Wat verstaan jy onder die term: “inspeksie”?

3. Wat beteken dit as ons sê “los die vergelyking op” ?

4. Gee ’n voorbeeld van ’n vergelyking.

5. Los nou die vergelyking in (4) op.

(Laat jou onderwyser jou help).

6. Los nou elk van die volgende vergelykings deur inspeksie, op.(m.a.w. bepaal die waarde van a)

6.1 1 - a = 7

6.2 5 a = 50

6.3 a /7 = 6

6.4 66/ a = 6

6.5 - a /2 = 15

6.6 5 a - 4 = 26

7. Hoe los jy ’n vergelyking op (nie deur inspeksie nie)

7.1 Hier is ’n paar wenke:

2a + 6 = -5 a - 9

Stap 1: Kry al die onbekendes (in die geval “ a ”) aan die linkerkant van die “=” teken.

Stap 2: Kry al die konstantes aan die regterkant van die “=” teken.

Stap 3: Tel gelyksoortige terme bymekaar.

Stap 4: Kry onbekende alleen (deur te × of te ÷ met koëffisiënt van onbekende)

Stap 1:

+5 a (moet aan anderkant dieselfde doen) +5 a (om van “ a ’s” ontslae te raak)

2 a + 6 = -5 a - 9

Nou lyk dit so: 2 a + 5 a + 6 = -9

Stap 2:

-6 (om van +6 ontslae te raak) -6 (moet aan anderkant dieselfde doen)

2 a + 5 a + 6 = -9

Nou lyk dit so: 2 a + 5 a = -9 - 6

Stap 3: Tel die soorte bymekaar

7 a = -15

Stap 4: Kry “ a ” alleen: ÷ 7 links en regs van “=” teken

7a 7 size 12{ { {"7a"} over {7} } } {} = -15 7 size 12{ { {"-15"} over {7} } } {}

a = 2 1 7 size 12{ - 2 { { size 8{1} } over { size 8{7} } } } {}

7.2 Wat van ?: a / 3 = 7

a / 3 = 7 / 1 (vermenigvuldig nou oorkruis)

a x 1 = 7 x 3

a = 21

7.3 Onthou indien hakies voorkom, moet die hakies eers verwyder word.bv.

2(2 a - 6) + 7 = 9 a - 3( a - 2)

4 a - 12 + 7 = 9 a - 3 a + 6

4 a - 3 a - 9 a = 6 - 7 + 12

-8 a = 11

a = 11 / -8

a = - 1 3 / 8

8. Doen jy nou die volgende: Los die volgende vergelykings op.

8.1 5 - 3(4 - a ) = 5( a + 1) + 2

8.2 2 a - 24 = 3 a

8.3 a / 4 + 5 = 10 (wenk: breuke en oorkruisvermenigvuldiging)

8.4 5 a - 3 a - 7 = 9

8.5 -8 a = 72

8.6 3² + 3 a + 3 = 2 3 + 4(-2 a )

8.7 -12 / a = -24

8.8 5(2 a + 1) = 4(2 a + 3)

8.9 -2(3 a - 3) = 6 a + 24

8.10 Stel enige vergelyking van jou keuse op en los dit dan op.

Voorwaardes: dit moet hakies bevat, breuke en negatiewe getalle.

KLASOPDRAG 2

  • Kom ontdek stap vir stap meer omtrent ... die oplos van woordprobleme, wat ’n fees word as jy dit as ’n vergelyking kan weergee.

Om in hierdie fees te kan deel, het jy die volgende basiese kennis nodig ......

1. Woorde soos ... meer (beteken +), minder (beteken -) en keer (beteken ×), opeenvolgende getalle (eerste getal: x , tweede getal: x + 1 en derde getal: x + 2)

1.1 Hoe sal jy drie opeenvolgende ewe getalle voorstel?

Eerste getal: …………… Tweede getal: …………… Derde getal: ……………

1.2 Hoe sal jy ’n tweesyfergetal voorstel indien die syfers onbekend is?

  • Wel, hoe sal jy 24 in uitgebreide notasie skryf: (2 x 10) + (4 x 1)
  • As daar gesê word die tiene syfer is die helfte van die ene syfer, sal jy as volg te werk gaan:

tiene ene

a 2 a (tiene syfer is helfte van ene syfer)

Dus: ( a x 10) + (2 a x 1) = 10 a + 2 a = 12 a (12 a is dan die getal)

2. Jou eerste vraag moet altyd wees: “Van watter een weet ek niks nie?”- dit word dan as (bv. x ) voorgestel, en die ander onbekendes in terme van ( x ).

3. Skryf dan ’n vergelyking neer .

Questions & Answers

where we get a research paper on Nano chemistry....?
Maira Reply
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
Google
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
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
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
Bob Reply
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?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Wiskunde graad 8. OpenStax CNX. Sep 11, 2009 Download for free at http://cnx.org/content/col11033/1.1
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