Question

What is the difference between an algebraic equation and an algebraic inequality?

Answer 1

Equations state precisely that two quantities are equal. Inequalities as the name suggests states that two quantities are not precisely equal. We can use this to find major differences between an equation and an inequality.

Complete step-by-step solution:
Let us first look at definitions of an algebraic equation and inequality. As the name suggests both of these deal with algebraic quantities. An equation is a statement which represents the equality of two quantities through an $=$ symbol, where the quantities on either side of the sign are equal.
On the other hand, an inequality basically states about two unequal quantities through the symbols
$<$ “less than”, $>$ “greater than”, $\ne$ “not equal”, $\leqslant$ “less than or equal to” and $\geqslant$ “greater than or equal to”. As their name suggests the symbols mean the relationship between the quantities which are not exactly equal. For example, $x \leqslant y$ implies that x is less than or equal to y.
The main difference between an equation and an inequality can be understood by the definitions itself, that is with the symbol used. But we will try to find other differences between them. Geometrically, an equation usually represents a curve (in case of equations with two unknown) and a surface (incase of equations with three unknowns). But an inequality represents a feasible region either above or below the curve representing the corresponding equation.
The solution set is a main difference between them as well. The possible number of solutions for a system of equations is either a finite number of points or an infinite collection of points (a curve – in case of equations where one is a scalar multiple of another). Whereas the solution of a system of inequalities is usually a region of the graph.

Note: Remember that when you multiply a negative quantity on both sides of an inequality the inequality is reversed, that is $<$ , $\leqslant$ turns into $>$ , $\geqslant$ and vice versa. There are a few more operations on inequalities where the inequality sign does not change.