Cambridge International Mathematics

90 Algebra (Equations and inequalities) (Chapter 3)

Example 20 Self Tutor

Solve forxand graph the solutions: a 3 x¡ 462 b 3 ¡ 2 x< 7

a 3 x¡ 462

) 3 x¡ 4 +4 62 +4 fadding 4 to both sidesg

) 3 x 66

)

3 x

3

6

6

3

fdividing both sides by 3 g

) x 62

Check: If x=1then 3 x¡4=3£ 1 ¡4=¡ 1 and¡ 162 is true.

b 3 ¡ 2 x< 7

) 3 ¡ 2 x¡ 3 < 7 ¡ 3 fsubtracting 3 from both sidesg

) ¡ 2 x< 4

)

¡ 2 x

¡ 2

>

4

¡ 2

fdividing both sides by¡ 2 ,

so reverse the signg

) x>¡ 2

Check: If x=3then 3 ¡ 2 x=3¡ 2 £3=¡ 3

and ¡ 3 < 7 is true.

Example 21 Self Tutor

Solve forxand graph the solutions: ¡ 5 < 9 ¡ 2 x

¡ 5 < 9 ¡ 2 x

) ¡ 5 +2x< 9 ¡ 2 x+2x fadding 2 xto both sidesg

) 2 x¡ 5 < 9

) 2 x¡ 5 +5< 9 +5 fadding 5 to both sidesg

) 2 x< 14

)

2 x

2

<

14

2

fdividing both sides by 2 g

) x< 7

Check: If x=5then ¡ 5 < 9 ¡ 2 £ 5 , i.e., ¡ 5 <¡ 1 which is true.

2 x

Notice the reversal of

the inequality sign in

line as we are

dividing by.

4

¡ 2

b

• 2 x

7 x

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Y:\HAESE\IGCSE01\IG01_03\090IGCSE01_03.CDR Friday, 12 September 2008 1:46:58 PM PETER