16.5  Vergelijkingen oplossen >
1
a

3 x 15 = 2 x 14
x 15 = 14
x = 1

b

3 x 5 = x + 1
2 x 5 = 1
2 x = 6
x = 3

c

3 x 5 = x 1
4 x = 4
x = 1

d

3 x + 15 = 2 x 3
x + 15 = 3
x = 18 , dus x = 18

2
a

x 2 16 = x 2 4 x + 4
16 = 4 x + 4
20 = 4 x
x = 5
controle:
( 5 + 4 ) ( 5 4 ) = 9 1 = 9
en
( 5 2 ) 2 = 3 2 = 9

b

2 x 2 ( x 2 + 2 x + 1 ) = x 2 4 x + 4
x 2 2 x 1 = x 2 4 x + 4
2 x 1 = 4 x + 4
2 x = 5
x = 2 1 2
controle:
2 ( 2 1 2 ) 2 ( 2 1 2 + 1 ) 2 = 2 6 1 4 ( 3 1 2 ) 2 = 12 1 2 12 1 4 = 1 4
( 2 1 2 2 ) 2 = ( 1 2 ) 2 = 1 4

c

4 ( x 2 2 x 3 ) = 4 x 2
4 x 2 8 x 12 = 4 x 2
8 x 12 = 0
8 x = 12
x = 1 1 2
controle:
4 ( 1 1 2 + 1 ) ( 1 1 2 3 ) = 4 ( 1 2 ) ( 4 1 2 ) = 9
( 2 1 1 2 ) 2 = ( 3 ) 2 = 9

d

x 2 + 5 x = x 2 + 6 x + 5
5 x = 6 x + 5
x = 5
x = 5
controle:
5 ( 5 + 5 ) = 5 0 = 0
( 5 + 1 ) ( 5 + 5 ) = 4 0 = 0

3
a

prijs fles sherry = 12 x
prijs fles cognac = 17 ( 12 x ) = 5 + x

b

vergelijking: x + ( 5 + x ) = 20
oplossing:
2 x + 5 = 20
2 x = 15
x = 7,50
wijn: € 7,50, sherry: € 4,50, cognac: € 12,50

4
a

Rechtsboven: breedte 10 x , hoogte x
Rechtsonder: breedte 10 x , hoogte 16 ( 10 x ) = 6 + x
Linksonder: hoogte 6 + x dus breedte 12 ( 6 + x ) = 6 x

b

De rechthoek met ? is dus x hoog en 6 x breed, de omtrek is dus 2 ( x + 6 x ) = 12 .

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5
a

3 x 9 + 4 x 7 6 + 2 x = 9 x 22

b

8 + 2 x 4 2 x + 14 = 18

c

2 x 3 x + 6 y 2 x 2 y = 3 x + 4 y

d

2 x y + x + 2 y + 2 x + 2 y = 5 x + 3 y

6
a

x + 2 4 x 8 = 6
3 x 6 = 6
3 x = 12
x = 4

b

4 x 6 30 x + 35 = 81 8 x
34 x + 29 = 81 8 x
26 x + 29 = 81
26 x = 52
x = 2

c

x 3 + 6 x + 12 = 7 x + 21
5 x + 9 = 7 x + 21
12 x = 12
x = 1

7
a

x 2

b

x + 5 , x 4

c

x 2 = ( x + 5 ) ( x 4 )

d

x 2 = ( x + 5 ) ( x 4 )
x 2 = x 2 + x 20
0 = x 20
x = 20
controle:
x 2 = 400
( x + 5 ) ( x 4 ) = 25 16 = 400

e

400 plaatsen

8
a

x 10 bij x + 12 meter

b

x 2 ; ( x 10 ) ( x + 12 )

c

x 2 = ( x 10 ) ( x + 12 )

d

x 2 = ( x 10 ) ( x + 12 )
x 2 = x 2 + 2 x 120
0 = 2 x 120
120 = 2 x
60 = x

e

De vierkante akker is 60 bij 60 meter.
De rechthoekige akker is 50 bij 72 meter.
De oppervlakte van beide akkers is 3600 m2.