Cambridge International Mathematics

Algebra (Equations and inequalities) (Chapter 3) 79

Example 5 Self Tutor

Solve forx: 5(x+1)¡ 2 x=¡ 7

5(x+1)¡ 2 x=¡ 7

) 5 x+5¡ 2 x=¡ 7

) 3 x+5=¡ 7 fcollecting like termsg

) 3 x+5¡ 5 =¡ 7 ¡ 5 fsubtracting 5 from both sidesg

) 3 x=¡ 12

)

3 x

3

=

¡ 12

3

fdividing both sides by 3 g

) x=¡ 4

When the unknown appears on both sides of the equation, remove it from one side. Aim to do this so the

unknown is left with apositivecoefficient.

Example 6 Self Tutor

Solve forx: 5 x+2=3x¡ 5

5 x+2=3x¡ 5

) 5 x+2¡ 3 x=3x¡ 5 ¡ 3 x fsubtracting 3 xfrom both sidesg

) 2 x+2=¡ 5

) 2 x+2¡ 2 =¡ 5 ¡ 2 fsubtracting 2 from both sidesg

) 2 x=¡ 7

)

2 x

2

=

¡ 7

2

fdividing both sides by 2 g

) x=¡ (^312)
Example 7 Self Tutor
Solve forx: 15 ¡ 2 x=11+x
15 ¡ 2 x=11+x
) 15 ¡ 2 x+2x=11+x+2x fadding 2 xto both sidesg
) 15 = 11 + 3x
) 15 ¡ 11 =11+3x¡ 11 fsubtracting 11 from both sidesg
) 4=3x
)

4

3

=

3 x

3

fdividing both sides by 3 g

) x=1^13

fgexpanding the brackets

IGCSE01

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Y:\HAESE\IGCSE01\IG01_03\079IGCSE01_03.CDR Monday, 15 September 2008 10:39:22 AM PETER