Cambridge International Mathematics

² if we want to findxsuch that f(x)< 0 , we graph y=f(x)and find values ofxwhere the function

isbelow thex-axis

² if we want to findxsuch that f(x)>g(x), we graph y=f(x) and y=g(x) on the same axes

and find values ofxfor which the graph of y=f(x) isabove y=g(x).

Example 1 Self Tutor

Solve the inequality: 5 ¡ 2 x¡x^2 < 0.

Using a graphics calculator we plot Y=5¡ 2 X¡X^2.

The graph cuts thex-axis when x¼¡ 3 : 45 and 1 : 45.

So, the solution is x<¡ 3 : 45 or x> 1 : 45

(to 3 significant figures).

Example 2 Self Tutor

Solve the inequality: 3+x> 2 x.

Using a graphics calculator we plot Y=2^X and

Y=3+X on the same set of axes.

Thex-coordinates of the points of intersection are:

x¼¡ 2 : 86 and 2 : 44.

The line y=3+x is above the exponential y=2x

when ¡ 2 : 86 <x< 2 : 44.

EXERCISE 32A

1 Solve forxusing technology:

a 1 ¡x< 3 b 3+x> 2 c 4 x¡ 1 > 5

d 2 ¡ 3 x 61 e^12 x¡ 1 > 0 f 3 ¡ 5 x 63 x+1

2

a x^2 ¡x¡ 6 > 0 b x^2 +x¡ 1260 c

d x^2 ¡ 2 x¡ 5 < 0 e 2 x^3 ¡ 5 x+6> 0 f x^3 ¡x^2 ¡ 2 x+1< 0

3 Solve forx:

a x^2 >x+3 b 3 x> 2 c 2 x> 4 ¡x^2

d x^2 > 2 x e 1 ¡x¡x^2 >

3

x

f

1

x

6 x^2 +1

4 Solve forx: sin(2x)> 0 : 461 for 0 o<x< 360 o

5 Solve forx: jxj+j 1 ¡ 2 xj< 3

O

y

x

-3 45. 1 45.

yxx¡=¡5¡-¡2 ¡-¡X

O x

y

-2 86-2 86.. 2.442.44

yx¡=¡3¡+¡

y¡=¡2x

Solve forx:

10 ¡x^2 ¡ 3 x> 0

640 Inequalities (Chapter 32)

IGCSE01

cyan magenta yellow black

(^05255075950525507595)
100 100
(^05255075950525507595)
100 100
Y:\HAESE\IGCSE01\IG01_32\640IGCSE01_32.CDR Monday, 27 October 2008 3:06:11 PM PETER