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How are equations different from inequalities?
Equations are statements that state two expressions are equal, while inequalities are statements that state two expressions are not equal, meaning one is greater or less than the other. The graph of the solution set of an equation is a line or a curve, while the graph of the solution set of an inequality is a region at one side of the boundary line or curve obtained by supposing that the inequality was an equation.
Is an equation true if the expressions on each side of the equal sign have the same value?
Yes, that is the point of equations. However, inequalities can also be manipulated to keep the indicator correct.
What are the similarities of equation and inequalities?
They both: - have variables, - are open sentences, - consist of two expressions joined by a "verb" (equals or inequality sign), - have solution sets (which may be empty or have one or more elements).
What are the two rules for inequalities which do not occur in equations?
Inequalities are not reflexive. Inequalities are not commutative.
Do solutions to systems of linear inequalities satisfy both inequalities?
Yes.
