Question

What is the difference between linear equations and linear inequalities?

Answer 1

It is easiest to describe the difference in terms of coordinate geometry.

A linear equation defines a straight line in the coordinate plane. Every point on the line satisfies the equation and no other points do.

For a linear inequality, first consider the corresponding linear equality (or equation). That defines a straight line which divides the plane into two. Depending on the direction of the inequality, all points on one side of the line or the other satisfy the equation, and no point from the other side of the line does. If it is a strict inequality (< or >) then points on the line itself are excluded while if the inequality is not strict (≤or ≥) then points on the line are included.