2.1 Vergelykings

6. Laat n enige natuurlike getal wees. As 3 die tienesyfer in n² is, bepaal die enesyfer in n².

7. Die gemiddelde van drie heelgetalle is 86. As een van hulle 70 is, wat is die gemiddelde van die ander twee?

8. Saretha het ’n R10- en R20-noot by ABSA omgeruil vir ’n gelyke aantal 50c-, 20c-, en 5c-stukke. Hoeveel muntstukke het Saretha gekry?

Assessering

Memorandum

1. - 5. Algemeen

6.1 1 – a = 7 a = –6

• a = 10
• 42 = a
• a = 11
• –30 = a
• a = 6

• 5 – 12 + 3 a = 5 a + 5 + 2

3 a – 5 a = 5 + 2 + 12 – 5

–2 a = 14

a = –7

• 2 a – 3 A = 24

– a = 24

$\therefore$ a = –24

8.3 $\frac{a}{4}$ = $\frac{5}{1}$ a = 20

8.4 2 a = 16

a = 8

• a = –9
• 9 + 3 a + 3 = 8 – 8 a

11 a = –4

$\therefore$ a = $\frac{-4}{\text{11}}$ (–2 $\frac{3}{8}$ )

8.7 $\frac{-\text{12}}{a}$ = $\frac{-\text{24}}{1}$ –24 a = –12

a = $\frac{1}{2}$

• 10 a + 5 = 8 a + 12

2 a = 7

a = 3 $\frac{1}{2}$

8.9 –6 a + 6 = 6 a + 24

–12 a = 18

a = $\frac{-\text{18}}{\text{12}}$ $\frac{-3}{2}$ (–1 $\frac{1}{2}$ )

• Eie keuse

KLASWERKOPDRAG 2

1. 20: 1. Nommer 1: x

Nommer 2: 15 – x

2. Kinders: x 20 x

Grootmense: (140 – x ) 45(140 – x )

20 x + 45(140 – x ) = 5 580

20 x + 6 300 – 45 x = 5 580

–25 x = –720

x = 28,8 28 / 29

Grootmense: 140 – 28 = 112

of 140 – 29 = 111

HUISWERKOPDRAG 1 EN 2

• –3 a = 3

a = –1

• a = –4

• 8 x – 21 x + 10 = 28

8(3) – 2(3) + 10 = 28

– 6 + 10 = 28 √

2.2 5 x – 10 = 10 x – 10

5 x – 10 x = –10 + 10

–5 x = 0

x = 0

x $$ 1R √

3.1 $\frac{1}{z}$ = $\frac{1}{\text{18}}$ $z$ = 18

3.2 1 – 5 z = 11

–5 z = 10

z = –2

3.2.1 Geen oplossing

3.2.2 z = –2

3.3 z + 3[ z + 2 z – 12] = 45

z + 3[3 z – 12] = 45

z + 9 z – 36] = 45

10 z = 81

z = 8,1

3.4 24 z – 32 – 2 z – 14 = 37

22 z = 83

z $$ 3,77

3.5 z – 5 z + 40 = 48

–7 z = –88

z = 22

• 6 x – 8 = 55

6 x = 63

x = 10 $\frac{1}{2}$ (10,5)

4.2 x + 9 x = –64

10 x = –64

x = –6,4

4.3 x + x 1 x + 2 = –90

3 x = –93

x = –31 –31; –30; 29

4.4 Lemoene: 3 x x 45 36

Piesangs: x x 18 12

18 x + 135 x = 1 836

153 x = 1 836

x = 12

• Nou –6

Cameron: x + 8 [ 18 ]; x + 8 –6

Liam: x [ 10 ]; x – 6

3( x – 6) = x + 2

3 x – 18 = x + 2

2 x = 20

x = 10

4.6 Seëls: R1,20 : x 50 – x

R2,40 : 50 – x of x

120 x + 240(50 – x ) = 5 880 1,20(50 – x ) + 2,40 x = 58,8

120 x + 12 000 – 240 x ) = 5 880 60 – 1,20 x ) + 2,40 x = 58,8

–120 x = –6 120 of 1,20 x = 1,20

x = 51 x = 1

R1,20 4

4.7 Een gedeelte: x

Ander gedeelte: x + 550

x + 2( x + 550) = 18 000

x 2 x + 1 100 = 18 000

3 x = 16 900

4.8 Massa

3 792 kgVrouens: 18 3 x

Dogters: 25 x

25 x + 3 x (18) = 3 792

25 x + 54 x = 3 792

79 x = 3 792

x = 48

Dogters: 48 kg elk

Vrouens: 144 kg elk

Nommer12 x 4.9 Ene: 2 x 8

Tiene x x 10 4

omgeruil: 21 x

2 x – 36 = 12 x

9 x = 36

x = 4

4.10 Gr. 8: x + 3 ² 257

Gr. 9: x 225

Gr. 10: x + 25 250

x + 32 + x + x + 25 = 732

3 x = 675

x = 225

TUTORIAAL 2

• Ya √ = Kan x se waarde uitwerk

[5 x = 5 ⁰ . x = 0]

• x = 0 √

• a = 12 √√
• a = 7 √√
• a = $\frac{7}{3}$ (2 $\frac{1}{3}$ ) √√
• a = 3 √√
• a = 4 √√

• 32 = 4(2(9) – p ) √

32 = 4(18 – p )

8 = 18 – p √

p = 10 √

• 45,67 = $\frac{p}{\text{21},3}$ √

p = 972,771 √

4.1 $\frac{\mathrm{7a}}{1}$ + $\frac{a}{3}$ = 30

$\frac{\text{22}a}{3}$ = $\frac{\text{30}}{1}$ √

22 a = 90 √

a = $\frac{\text{90}}{\text{22}}$

= 4 $\frac{2}{\text{22}}$ = 4 $\frac{1}{\text{11}}$ √

4 a ² – 3 a = 4 a ^{2 √} √

0 = 3 a √

1. = a √
3. –4 a + 8 = 3 a – 12 √

–7 a = –20 √

a = $\frac{\text{20}}{7}$ = 2 $\frac{6}{7}$ (of $$ 2,86) √

• 5 a + 15 + 4 a + 5 = 2 a – 14 √

7 a = –34 √

a = 4,9 √

• 5 a = –2 a + 6 √

7 a = 6 √

a = $\frac{6}{7}$ (0,86) √

• 9 x – 28 = 5 x √

4 x = 28

x = 7 √

5.2.1 x + 4 2 x + 2( x + 4) = 108 √

2 x + 2 x + 8 = 108

4 x = 100

x = 25√

√ √

$\therefore$ l = 29 cm b = 25 cm

5.2.2 A = 29 x 25 √

= 725 cm ² √

6. x + x + 2 + x + 4 + x + 6 = 112 √

4 x = 112 – 12

4 x = 100

x = 25 √

$\therefore$ Nommers: 25; 27; 29; 31 √√

7. $\sqrt{\text{6162}}$ $$ 78 √

$\therefore$ 6 162 ÷ 78 = 79

$\therefore$ 78; 79 √√

TOETS 1

1.11 x = 34

1.12 –3 x = 1

–3 x = –6

$\therefore$ x = 2

1.13 2 x + 10 = 18

2 x = 8

$\therefore$ x = 4

1.14 2 x = 40 – 8

2 x = 32

$\therefore$ x = 16

• x – 6 – x – 1 = 5 x – 4

2 x – x – 5 x = –4 + 1 + 6

–4 x = 3

x = $\frac{-3}{4}$

• 3 x = 15 – 6

3 x = 9

$\therefore$ x = 3

1.7 x = 4 x 2 = 8

1.8 6 x + 48 = 114

6 x = 66

$\therefore$ x = 11

1.9 x – 7 x = 30 – 9

3 x = 21

$\therefore$ x = 7

1.10 x – 2 – 2 x 3 = 7

– x = 7 + 3 + 2

– x = 12

$\therefore$ x = –12

• $\left(\frac{x-5}{3}\right)$ = 4

x = (4 × 3) + 5

= 17

• x + x 1 + x + 2 = 66

3 x = 63

x = 21

• 2 x + 2( x + 5,5) = 27

2 x + 2 x + 11 = 27

4 x = 16 x 4 cm

x = 4 x + 5,5 9,5 cm

2.4 Jonte: 5 x 50 5 x + x = 60

Dogters: x 10 6 x = 60

x = 10

2.5 Nou +5

Gareth 5 x 5 x + 5

Seun x x + 5

$\therefore$ Gareth: 25

$\therefore$ Seun: 5 x + 5 = 3( x + 5)

5 x + 5 = 3 x + 15

2 x = 10

x = 5

3. $(\frac{1}{\mathrm{2a}}$ + 2 $a)$ ² = 7 ²

$\frac{1}{{\mathrm{4a}}^2}$ + 2 + 4 $a$ ² = 49

$\frac{1}{{\mathrm{4a}}^2}$ + 4 $a$ ² = 47