Page 28 - MAT KS3 Y8 Cambridge CheckPoint

2.5 Constructing linear expressions

2.5 Constructing linear expressions

You can write an algebraic expression by using a letter to represent an unknown number.
The letter is called the variable.
Example: Let n represent a mystery number.
You write the number that is five more than the mystery number as n + 5 or 5 + n.
You write the number that is three times the mystery number as 3 × n or simply 3n.
2
You write the mystery number multiplied by itself as n × n or simply n .
n + 5 and 3n are called linear expressions because the variable is only
n + 5 is the same as 1 × n + 5.
multiplied by a number.
2
n is not a linear expression because the variable is being multiplied by itself.

Worked example 2.5

Tyler thinks of a number, x. Write down an expression for the number Tyler gets when he:
a subtracts 5 from the number b doubles the number and adds 3
c divides the number by 3 and adds 2 d adds 2 to the number then multiplies by 4.

a x – 5 Subtract 5 from x.
b 2x + 3 Multiply x by 2, then add 3. Write 2 × x as 2x.
x x
c + 2 Divide x by 3 then add 2. Write x ÷ 3 as .
3 3
d 4(x + 2) Add 2 to x, then multiply the answer by 4. Write x + 2 in brackets to show this must be done
before multiplying by 4.

✦ Exercise 2.5

1 Tanesha has a box that contains x DVDs.
In each part of the question
Write an expression for the total number of DVDs she has in the
she starts with x DVDs.
box when:
a she takes 7 out b she puts in 8 more
c she takes out half of them d she doubles the number in the box and adds an extra 1.

2 Jake thinks of a number, n.
Write an expression for the number Jake gets when he:
a multiplies the number by 6 then adds 1 b divides the number by 4 then adds 5
c multiplies the number by 2 then subtracts 3 d divides the number by 10 then adds 7.
3 The price of one bag of cement is $c.
The price of one bag of gravel is $g.
The price of one bag of sand is $s.
Write an expression for the total cost of:
a one bag of cement and three bags of sand
b three bags of cement, four bags of gravel and 6 bags of sand.
4 Alicia thinks of a number, n. She subtracts 3 then multiplies the result by 2.
Which of these expressions is the correct expression for Alicia’s number? Explain your answer.

A n – 3 × 2 B n – 6 C 2(n – 3) D 3 – n × 2 E 2(3 – n)

26 2 Sequences, expressions and formulae