Basic Algebra


Introduction


The letter 'x' is a very common symbol used in algebra to represent an unknown quantity. For this reason it is wise to avoid use of the similar multiplication sign. Usually the multiplication sign is 'understood', e.g

5x

actually represents

5 × x

in the 'old' representation.

If it is really necessary to use a specific sign to denote multiplication, then the use of the 'full-stop' or brackets is to be recommended, i.e. instead of

5 × 3

use

5 . 3

(but this is only where no confusion would arise with a decimal point!)

or

(5)(3)

Question

(a) A cup of tea costs 80 pence.

Write down an expression, in terms of x, for the cost, in pence, of x cups of tea.

(b)A cup of coffee costs 95 pence.

Write down an expression, in terms of y, for the cost, in pence, of y cups of coffee.

. (c) Write down an expression, in terms of x and y, for the total cost, in pence, of x cups of tea and y cups of coffee.

Answer

(a) 80x

(b) 95y

(c) 80x + 95y

Substitution

Proceed by example

Example What is the value of

3x - 4y

when x=3 and y=2?

Answer

3x - 4y

= 3(3) - 4(2)

= 9 - 8

= 1

Example What is the value of


when p=2 and q = -7?

Answer