unit 2 sec 4.1

Unit 2 sec 4.1 notation for working with inequalities

30 October 2015

21:52

This section considers some notation that can be used for describing a range of possible values that variable can take. In order to describe known restrictions on the variables, and when stating your conclusions. The restrictions on a variable that represents the speed of a car might be that it is greater than or equal to zero and then or equal to the speed limit that applies.

 The nature of this inequality can be expressed by using the phrases less than an greater than or the inequality signs < and >.

   If a number way to the life of another number on the number line, then it is said to be less than the number. -5 lives to the left of -2, as shown in figure 14, so -5 is less than -2. This statement can be written more concisely by using the inequality sign < for less than;

 -5 < -2

#rise to the right of another number on the number line, then it is said to be greater than the other number. -1 lies to the right of -3, -1 is greater than -3. This statement can be written using the inequality sign > for greater than.

-1 > -3

in a statement involving inequality signs is cold and inequality. Each inequality can be written into different ways. For example 4 is greater than 2 so you can write

4 > 2

but also 2 is less than 4, so you can write.

2 < 4

each way of writing and inequality is obtained from the other by swapping the numbers and reversing the inequality sign. This is called reversing the inequality.

As well as the 2 inequality signs introduced above, there are 2 other inequality signs, ≤ and ≥. Before inequality signs and their meanings are given in the following box.

Inequality signs

< is less than

≤is less than or equal to

>      is greater than

≥ is greater than or equal to

here are some examples of correct inequalities

Ø 1 <1.5, because one is worse than 1.5

Ø 1 ≤ 1.5, because one is less than or equal to 1.5 (it is ‘less than’ 1.5).

Ø 1 ≤ 1, because one is less than or equal to 1 (it is ‘equal to’1).

It may seem strange to write 1 ≤ 1.5 and 1 ≤ 1, when the more precise statements 1<1.5 and 1 = 1 can be made, and you would not usually right. The former statements. The inequality signs ≤ and ≥ are useful, however, for specifying the range of values that the valuable intake, as in the following example.

Example 14 specifying the range of variable

suppose that the speed of a car on the UK motorway is s km/h. Write down to inequalities that specify the range of possible legal values of s.

Solution

first, decide what you want to say in words.

This speed must be greater than or equal to 0 and should be less than or equal to the speed limit on the UK motorway, that is, 112 km/h (70 mph).

Replace the words by the appropriate inequalities.

So the two inequalities are

S ≥ 0 and s ≤ 112.

Most inequalities that you will meet involve variables. The value of the variable for which the inequality is true, is said to satisfy the inequality.