Algebra Inequalities

The Concept Of Inequalities

An inequality is a relationship between two quantities that are not equal.

The symbols used for inequality are:

> means ‘greater than’

< means ‘less than’

≥ means ‘greater than or equal to’

≤ means ‘less than or equal to’

Linear Inequality In One Variable

In equations, one side is equal to the other side. In linear inequalities, one side is bigger than or smaller than or equal to the other side.

A linear equation in one variable has only one solution. An inequality in one variable has a set of possible solutions.

Example:

Given that x is an integer. State the possible integer values of x in the following inequalities.

a) x > 4

b) x ≤ –3

Solution:

a) x is greater than 4.

5, 6, 7, 8, …

b) x is less than or equal to –3

–3, –4, –5, –6, …

Using The Number Line To Represent Inequalities

We can represent a linear inequality in one variable on a number line. We use the following symbols in the representation.

A small circle is used for < and > to indicate that the number is not included.

A filled-in circle is used for ≤ and ≥ to indicate that the number is included.

A line with an arrow indicates that the line continues to infinity in the direction of the arrow.

Example:

Represent each inequality on a number line.

a) x ≤ 0

b) x > 2

c) x < 1

d) x ≥1

Solution:

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