Learners are expected to recall the interpretation of the inequality symbols <, ≤, > and ≥. If the equality symbol (=) in a linear equation ax+b = 0 is replaced by any one of the inequality symbols (< , ≤, >, ≥), then we get a linear inequality as defined below.

Definition

An inequality in one variable, say say x, that can be written in the form
ax + b < 0 (or with any one of ≤, > or ≥ at the place of < )
where a and b are specified numbers such that a ≠ 0, is called linear inequality.

For instance,

are examples of a linear inequality.

Note that while an equality such as x = 5 represents exactly one value, an inequality, say x < 5, represents (satisfied by) several numbers such as 4.99, 4, 3.5, 1, 0, −2, etc. The solution of an inequality is the set of all values of the variable that satisfy the inequality, that is, the set of all values of the variable for which the inequality is true. This set is called the truth set (or solution set) of the inequality. For instance, the truth set of x < 5 is {x∈ℝ | x < 5}. That is, every real number below 5 satisfies the inequality.