Solution Set of an The set of all values of the variable that make the inequality a true Inequality statement Solving an inequality Finding the solution set of the inequality Inequality Properties: If a, b, and c are any real numbers, Transitive Property If a < b and b < c, then a < c If a < b, then a + c < b + c Addition Property Add the same value to BOTH sides of an inequality If a < b, then a c < b c Subtraction Property – – Subtract the same value from BOTH sides of an inequality a b c ca cb If < and is positive, then < Multiplying the same POSITIVE value on BOTH sides of an inequality will NOT change the inequality. Multiplication Property If a < b and c is negative, then ca > cb Multiplying the same NEGATIVE value on BOTH sides of an inequality WILL REVERSE the inequality symbol. If a < b and c is positive, then Dividing the same POSITIVE value on BOTH sides of an inequality will NOT change the inequality. Division Property If a < b and c is negative, then Dividing the same NEGATIVE value on BOTH sides of an inequality WILL REVERSE the inequality symbol. Examples:
Solution Set of an Inequality The set of all values of the variable that make the inequality a true statement Solving an inequality Finding the solution set of the inequality Inequality Properties: If a, b, and c are any real numbers, Transitive Property If a < b and b < c, then a < c Addition Property If a < b, then a + c < b + c Add the same value to BOTH sides of an inequality Subtraction Property If a < b, then a – c < b – c Subtract the same value from BOTH sides of an inequality Multiplication Property If a < b and c is positive, then ca < cb Multiplying the same POSITIVE value on BOTH sides of an inequality will NOT change the inequality. If a < b and c is negative, then ca > cb Multiplying the same NEGATIVE value on BOTH sides of an inequality WILL REVERSE the inequality symbol. Division Property If a < b and c is positive, then Dividing the same POSITIVE value on BOTH sides of an inequality will NOT change the inequality. If a < b and c is negative, then Dividing the same NEGATIVE value on BOTH sides of an inequality WILL REVERSE the inequality symbol. Examples:
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