An inequality is a mathematical relationship between two expressions and is represented using one of the following:
Inequalities involving "<", "≠" or ">" are referred to as "strict inequalities", while inequalities involving "≤" or "≥" are not.
If you "switch" the two sides of an inequality you must then reverse the direction of the inequality symbol. For example since it is true that 4 < 5, it is also true that 5 > 4.
An equation is a statement of equality between two expressions. An equation uses the equality symbol (=).
Like solutions to conditional equations, solutions to inequalities in one variable can be represented using a number line.
When considering locations along a number line, the inequality symbols can be interpreted as follows:
Strict inequalities are usually used when no variables are involved.
Inequalities involving a variable are sometimes referred to as "inequations".
At the present time, the term "inequality" refers to both inequations (with a variable) and simple inequalities without a variable.
-2 < 2: -2 is to the left of +2 on the number line (as shown below).
Adding or subtracting either a positive or negative number to each side of the inequality will result in a true statement.
For example, if you add one to each side of the inequality (or equivalently subtract negative one from each side of the inequality), the following occurs:
If you add negative one to each side of the inequality (or equivalently subtract positive one from each side of the inequality), the following occurs:
If you multiply each side of the inequality by two, the following occurs:
If you multiply each side of the inequality by negative two, the following occurs:
Note that the result of multiplying (or dividing) both sides of a (true) inequality by a negative number is an inequality which is false, unless you reverse the direction of the inequality.
It is important to keep this in mind when solving an inequality such as -2x + 7 ≥ 25.