Unit 2 sec 4.2

Unit 2 sec 4.2 illustrating Inequality on a number line

30 October 2015

22:48

And inequality can be represented on a number line by making this section of the number line where the inequality is true. Section of the number line without any gaps is shown as an interval. So illustrates the inequality s ≤ 112. The small solid circle at the limit 112 indicates that 112 is contained in the interval and is a possible value for s.

A straight inequality can be represented on a number line by using a small empty circle at the limit. The possible value for u line it to the right of 4.

Example 15 using a double inequality

the child is 5 years or older, but not yet 16 is eligible for child fare on the train. Children under 5 travel free. Suppose that a represents the age of the child in years.

(A)       draw a number line to illustrate the ages eligible for a child fare.

(B)         Give double inequality to describe the age restriction for child fares. Which whole number satisfy this inequality?

Solution

(A)       mark the limits at 5 and 16 on the number line first, and then join the limits with the line.

The ages of children who are eligible for a child there, as shown on the number line.

(B)         the restrictions of the age for a child there are

a is greater than or equal to 5, and a is less than 16.

Using inequality signs,

a ≥ 5 and a ≤ 16

 Now, a ≥ 5 and a ≤ 16

therefore, the inequalities are

5 ≤ a and a < 16.

These two inequalities can be combined as the double inequality

 5 ≤ a < 16.

The whole numbers satisfy this inequality are

5,6,7,8,9,10,11,12,13,14,15.

The double inequality 5 ≤ a < 16 is read as

‘5 is less than or equal to a, which is less than 16’, or as

‘a is greater than or equal to 5, and worse than 16’.

Inequalities can also be used to illustrate the range of possible numbers that round to a particular value.