integers: they are whole numbers which are not fractions
inequalities: they are different in size, cirumstances, degrees, lack of equality, etc.
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Inequalities are not reflexive. Inequalities are not commutative.
Yes.
equations have an = sign, inequalities do not
Yes.
An inequality with "and" is true if BOTH inequalities are true. Inequality with "or" is true if ONE of the inequalities are true.