Cambridge International Mathematics

80 Algebra (Equations and inequalities) (Chapter 3)

Summary Step 1: If necessary,expandanybracketsandcollect like terms.

Step 2: If necessary, remove the unknown from one side of the equation.

Aim to do this so the unknown is left with apositivecoefficient.

Step 3: Use inverse operations toisolate the unknownand maintain balance.

Step 4: Checkthat your solution satisfies the equation, i.e., LHS=RHS.

EXERCISE 3A.2

1 Solve forx:

a 3(x¡2)¡x=12 b 4(x+2)¡ 2 x=¡ 16 c 5(x¡3) + 4x=¡ 6

d 2(3x+2)¡x=¡ 6 e 5(2x¡1)¡ 4 x=11 f ¡2(4x+3)+2x=12

2 Solve forx:

a 3(x+2)+2(x+4)=¡ 1 b 5(x+1)¡3(x+2)=11 c 4(x¡3)¡2(x¡1) =¡ 6

d 3(3x+1)¡4(x+1)=14 e 2(3 + 2x)+3(x¡4) = 8 f 4(5x¡3)¡3(2x¡5) = 17

3 Solve forx:

a 5 x+2=3x+14 b 8 x+7=4x¡ 5 c 7 x+3=2x+9

d 3 x¡8=5x¡ 2 e x¡3=5x+11 f 3+x=15+4x

4 Solve forx:

a 6+2x=15¡x b 3 x+7=15¡x c 5+x=11¡ 2 x

d 17 ¡ 3 x=4¡x e 8 ¡x=x+6 f 9 ¡ 2 x=3¡x

5 Solve forx:

a 2(x+4)¡x=8 b 5(2¡ 3 x)=¡ 8 ¡ 6 x c 3(x+2)¡x=12

d 2(x+1)+3(x¡4) = 5 e 4(2x¡1) + 9 = 3x f 11 x¡2(x¡1) =¡ 5

g 3 x¡2(x+1)=¡ 7 h 8 ¡(2¡x)=2x i 5 x¡4(4¡x)=x+12

j 4(x¡1) = 1¡(3¡x) k 3(x¡6) + 7x= 5(2x¡1) l 3(2x¡4) = 5x¡(12¡x)

More complicated fractional equations can

be solved by:

² writing all fractions with the lowest

common denominator (LCD)and then

² equating numerators.

B SOLVING EQUATIONS WITH FRACTIONS [2.3]

To solve equations

involving fractions, we

make the denominators

the same so that we can

equate the numerators.

IGCSE01

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Y:\HAESE\IGCSE01\IG01_03\080IGCSE01_03.CDR Friday, 12 September 2008 12:13:02 PM PETER