Maths:Topic Five: "Inequality"

Topic Five: "Inequality"

Introduction:

The expression 5x − 4 > 2x + 3 looks like an equation but with the equals sign replaced by an
arrowhead. It is an example of an inequality.

This denotes that the part on the left, 5x − 4, is greater than the part on the right, 2x + 3. We
will be interested in finding the values of x for which the inequality is true.

We use four symbols to denote inequalities:

Key Point

>  is greater than

> is greater than or equal to

<  is less than

< is less than or equal to

Notice that the arrowhead always points to the smaller expression

EXAMPLES:

1. We can solve this by subtracting 3 from both sides:

x + 3 > 2

x > −1

So the solution is x > −1. This means that any value of x greater than −1 satisfies x + 3 > 2.
Inequalities can be represented on a number line such as that shown in Figure 1. The solid line
shows the range of values that x can take. We put an open circle at −1 to show that although
the solid line goes from −1, x cannot actually equal −1.

Figure 1. A number line showing x > −1.

2. Suppose we wish to solve the inequality

4x + 6 > 3x + 7.

First we subtract 6 from both sides to give

4x > 3x + 1

Now we subtract 3x from both sides:

x > 1

This is the solution. It can be represented on the number line as shown in Figure 2.

Figure 2. A number line showing x > 1.

REFERENCE:

www.mathcentre.ac.uk/resources/uploaded/mc-ty-inequalities-2009-1.pdf