Cambridge International Mathematics

Algebra (Equations and inequalities) (Chapter 3) 83

g

2 x¡ 7

3

¡1=

x¡ 4

6

h

x+1

3

¡

x

6

=

2 x¡ 3

2

i

x

5

¡

2 x¡ 5

3

=

3

4

j

x+1

3

+

x¡ 2

6

=

x+4

12

k

x¡ 6

5

¡

2 x¡ 1

10

=

x¡ 1

2

l

2 x+1

4

¡

1 ¡ 4 x

2

=

3 x+7

6

Algebraic equationsare mathematical sentences which indicate that two

expressions have the same value. They always contain the “=” sign.

Many problems we are given are stated in words. Before we can solve a worded problem, we need to

translate the given statement into a mathematical equation. We then solve the equation to find the solution

to the problem.

The followingstepsshould be followed:

Step 1: Decide what the unknown quantity is and choose a variable such asxto represent it.

Statement Translation

decreased by subtract

more than add

double multiply by 2

halve divide by 2

Step 2: Look for the operation(s) involved in the problem.

For example, consider the key words in the table

opposite.

Step 3: Form the equation with an “=” sign. These phrases indicate equality:

“the answer is”, “will be”, “the result is”, “is equal to”, or simply “is”

Example 11 Self Tutor

Translate into an equation:

a “When a number is added to 6 , the result is 15 .”

b “Twice a certain number is 7 more than the number.”

a In words

“a number”

“a number is added to 6 ”

“the result is”

Indicates

We letxbe the number

6+x

6+x=

So, 6+x=15

b In words

“a certain number”

“twice a certain number”

“ 7 more than the number”

“is”

Indicates

Letxbe the number

2 x

x+7

So, 2 x=x+7

C FORMING EQUATIONS

In the following

exercise, you do not

have to set out your

answers like those

given in the example.

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Y:\HAESE\IGCSE01\IG01_03\083IGCSE01_03.CDR Friday, 12 September 2008 12:21:40 PM PETER