Cambridge International Mathematics

Algebra (Equations and inequalities) (Chapter 3) 77

Example 1 Self Tutor

The inverse

operation for+7

is¡ 7.

Solve forx: 3 x+7=22

) 3 x+7=22

) 3 x+7¡ 7 =22¡ 7 fsubtracting 7 from both sidesg

) 3 x=15 fsimplifyingg

)

3 x

3

=

15

3

fdividing both sides by 3 g

) x=5 fsimplifyingg

Check: LHS=3£5+7=22 ) LHS=RHS X

Example 2 Self Tutor

Solve forx: 11 ¡ 5 x=26

11 ¡ 5 x=26

) 11 ¡ 5 x¡ 11 =26¡ 11 fsubtracting 11 from both sidesg

) ¡ 5 x=15 fsimplifyingg

)

¡ 5 x

¡ 5

=

15

¡ 5

fdividing both sides by¡ 5 g

) x=¡ 3 fsimplifyingg

Check: LHS=11¡ 5 £¡3 = 11+15 = 26 ) LHS=RHS X

Example 3 Self Tutor

x

3

is really

x¥ 3. The

inverse operation

of¥ 3 is£ 3.

Solve forx:

x

3

+2=¡ 2

x

3

+2=¡ 2

)

x

3

+2¡ 2 =¡ 2 ¡ 2 fsubtracting 2 from both sidesg

)

x

3

=¡ 4

)

x

3

£ 3 =¡ 4 £ 3 fmultiplying both sides by 3 g

) x=¡ 12

Check: LHS=¡^123 +2=¡4+2=¡2=RHS. X

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Y:\HAESE\IGCSE01\IG01_03\077IGCSE01_03.CDR Friday, 12 September 2008 12:06:41 PM PETER