Final answer:
Properties of equality and properties of inequality are used when solving equations and inequalities in mathematics.
Step-by-step explanation:
When solving equations and inequalities, properties of equality and properties of inequality are used. Properties of equality include the reflexive property, symmetric property, transitive property, addition property of equality, and multiplication property of equality. These properties state that if two quantities are equal, then they can be replaced by each other in an equation.
On the other hand, properties of inequality include the addition property of inequality and the multiplication property of inequality. These properties state that if the same real number is added to or multiplied by both sides of an inequality, the inequality remains true. However, when multiplying or dividing both sides of an inequality by a negative number, the direction of the inequality symbol must be flipped.
Learn more about Properties of equality and properties of inequality