Cambridge International Mathematics

Algebra (Equations and inequalities) (Chapter 3) 89

EXERCISE 3F

1 Represent the following inequalities on a number line:

a x> 5 b x> 1 c x 62 d x<¡ 1

e ¡ 26 x 62 f ¡ 3 <x 64 g 16 x< 6 h ¡ 1 <x< 0

i x< 0 or x> 3 j x 6 ¡ 1 or x> 2 k x< 2 or x> 5 l x 6 ¡ 2 or x> 0

2 Write down the inequality used to describe the set of numbers:

abc

de f

gh i

jk l

Notice that 5 > 3 and 3 < 5 ,

and that ¡ 3 < 2 and 2 >¡ 3 :

This suggests that if weinterchangethe LHS and RHS of an inequation, then we mustreversethe inequality

sign. >is the reverse of<, >is the reverse of 6 , and so on.

You may also remember from previous years that:

² If weaddorsubtractthe same number to both sides, the inequality sign ismaintained.

For example, if 5 > 3 then 5 +2> 3 +2.

² If wemultiplyordivideboth sides by apositivenumber, the inequality sign ismaintained.

For example, if 5 > 3 then 5 £ 2 > 3 £ 2 :

² If wemultiplyordivideboth sides by anegativenumber, the inequality sign isreversed.

For example, if 5 > 3 then 5 £¡ 1 < 3 £¡ 1 :

The method of solution of linear inequalities is thus identical to that of linear equations with the exceptions

that:

² interchangingthe sidesreversesthe inequality sign

² multiplyingordividingboth sides by anegativenumberreversesthe inequality sign.

G SOLVING LINEAR INEQUALITIES [2.2]

x

0

5

x

-5

4

x

-1

20

x

7

10

x

3

x

-2

x

100

x

0.2

7

x

2

0

x

-3 17

x

4 33

x

21

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Y:\HAESE\IGCSE01\IG01_03\089IGCSE01_03.CDR Wednesday, 17 September 2008 9:26:58 AM PETER