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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 .

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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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