Cambridge International Mathematics

78 Algebra (Equations and inequalities) (Chapter 3)

Example 4 Self Tutor

Solve forx:

4 x+3

5

=¡ 2

4 x+3

5

=¡ 2

) 5 £

(4x+3)

5

=¡ 2 £ 5 fmultiplying both sides by 5 g

) 4 x+3=¡ 10

) 4 x+3¡ 3 =¡ 10 ¡ 3 fsubtracting 3 from both sidesg

) 4 x=¡ 13

)

4 x

4

=¡

13

4

fdividing both sides by 4 g

) x=¡ (^314)
EXERCISE 3A.1
1 Solve forx:
a x+11=0 b 4 x=¡ 12 c 5 x+35=0 d 4 x¡5=¡ 17
e 5 x+3=28 f 3 x¡9=18 g 8 x¡1=7 h 3 x+5=¡ 10
i 13 + 7x=¡ 1 j 14 = 3x+5 k 4 x¡7=¡ 13 l ¡3=2x+9
2 Solve forx:
a 8 ¡x=¡ 3 b ¡ 4 x=22 c 3 ¡ 2 x=11 d 6 ¡ 4 x=¡ 8
e 3 ¡ 7 x=¡ 4 f 17 ¡ 2 x=¡ 5 g 15 = 3¡ 2 x h 24 ¡ 3 x=¡ 9
i 4=3¡ 2 x j 13 =¡ 1 ¡ 7 x k ¡21 = 3¡ 6 x l 23 =¡ 4 ¡ 3 x
3 Solve forx:
a
x
4
=7 b
2 x
5
=¡ 6 c
x
2
+3=¡ 5 d
x
4

¡2=¡ 5

e

x¡ 1

3

=6 f

x+5

6

=¡ 1 g 4=

2+x

3

h ¡1+

x

3

=7

4 Solve forx:

a

2 x+11

3

=0 b^12 (3x+1)=¡ 4 c

1+2x

5

=7 d

1 ¡ 2 x

5

=3

e^14 (1¡ 3 x)=¡ 2 f^14 (5¡ 2 x)=¡ 3

EQUATIONS WITH A REPEATED UNKNOWN

Equations where the unknown appears more than once need to be solved systematically. Generally, we:

² expand any brackets

² collect like terms

² use inverse operations to isolate the unknown while at the same time maintaining the balance of the

equation.

IGCSE01

cyan magenta yellow black

(^05255075950525507595)
100 100
(^05255075950525507595)
100 100
Y:\HAESE\IGCSE01\IG01_03\078IGCSE01_03.CDR Monday, 15 September 2008 10:38:59 AM PETER