Cambridge International Mathematics

82 Algebra (Equations and inequalities) (Chapter 3)

Example 10 Self Tutor

Solve forx:

3 x+1

x¡ 1

=¡ 2

3 x+1

x¡ 1

=

¡ 2

1

fLCD=x¡ 1 g

)

3 x+1

x¡ 1

=

¡ 2 £(x¡1)

1 £(x¡1)

fto achieve a common denominatorg

) 3 x+1=¡2(x¡1) fequating numeratorsg

) 3 x+1=¡ 2 x+2 fexpanding bracketsg

) 3 x+1+2x=¡ 2 x+2+2x fadding 2 xto both sidesg

) 5 x+1=2

) 5 x+1¡ 1 =2¡ 1 fsubtracting 1 from both sidesg

) 5 x=1

) x=^15 fdividing both sides by 5 g

EXERCISE 3B

1 Solve forx:

a

2 x+3

5

=

1

2

b

x+6

2

=

x

3

c

2 x¡ 11

7

=

3 x

5

d

x+4

2

=

2 x¡ 3

3

e

3 x+2

2

=

x¡ 1

4

f

1 ¡x

2

=

x+2

3

g

x+5

2

=1¡x h

2 x+7

3

=x+4 i

2 x+9

2

=x¡ 8

2 Solve forx:

a

3

x

=

1

5

b

3

x

=

2

3

c

2

7

=

5

x

d

4

9

=

1

x

e

1

2 x

=

4

3

f

7

3 x

=¡ 4 g

4

5 x

=3 h ¡5=

2

3 x

3 Solve forx:

a

3 x¡ 11

4 x

=¡ 2 b

2 x+7

x¡ 4

=¡ 1 c

2 x+1

x¡ 4

=4

d

2 x

x+4

=3 e

¡ 3

2 x¡ 1

=5 f

4 x+1

x+2

=¡ 3

4 Solve forx:

a

x

2

¡

x

6

=4 b

x

4

¡3=

2 x

3

c

x

8

+

x+2

2

=¡ 1

d

x+2

3

+

x¡ 3

4

=1 e

2 x¡ 1

3

¡

5 x¡ 6

6

=¡ 2 f

x

4

=4¡

x+2

3

IGCSE01

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Y:\HAESE\IGCSE01\IG01_03\082IGCSE01_03.CDR Friday, 12 September 2008 12:19:34 PM PETER