Cambridge International Mathematics

88 Algebra (Equations and inequalities) (Chapter 3)

EXERCISE 3E

1 Solve forx, giving your answers correct to 3 significant figures:

a x^2 =11 b x^2 =¡ 5 c x^2 =71 d x^2 =89, x> 0

e x^3 =8 f x^3 =11 g x^3 =¡ 11 h x^4 =81

i x^4 =¡ 1 j x^5 =23 k x^5 =¡ 113 l x^6 =39: 2 , x> 0

2 Solve forx:

a

x

3

=

4

x

b

x

6

=

6

x

c

1

x

=

x

3

d

x

7

=

7

x

e

2

x

=

x

5

f

7

x

=

x

5

g

x

2

=

8

x

h

x

5

=

¡ 2

x

The speed limit when passing roadworks is often 25 kilometres per hour.

This can be written as alinear inequalityusing the variablesto represent the speed

of a car in km per h. s 625 reads ‘sis less than or equal to 25 ’.

We can also represent the allowable speeds on anumber line:

The number line shows that any speed of 25 km per h or less is an acceptable speed.

We say that these aresolutionsof the inequality.

REPRESENTING INEQUALITIES ON A NUMBER LINE

Suppose our solution to an inequality is x> 4 ,soeverynumber which is 4 or greater than 4 is a possible

value forx. We could represent this on a number line by:

Likewise if our solution is x< 5 our representation would be:

Example 19 Self Tutor

Represent the following inequalities on a number line:

a 16 x< 5 b x< 0 or x> 4

ab

F INTERPRETING LINEAR INEQUALITIES [2.1]

4

The filled-in circle indicates

that 4isincluded.

The arrowhead indicates that all numbers on

the number line in this direction are included.

x

5

The hollow circle indicates that 5is notincluded.

x

25

25

s

0

5

x

1 4

x

0

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Y:\HAESE\IGCSE01\IG01_03\088IGCSE01_03.CDR Friday, 12 September 2008 12:51:23 PM PETER