INEQUALITIES An inequality is a relationship in which two quantities may not be equal. Phrases such as “at most” and “at least” suggest this type of relationship
WRITING & GRAPHINGINEQUALITIES
WRITE THE INEQUALITYTHAT REPRESENTS THESENTENCE. 5 fewer than a number is at least 12 The product of a number and 8 is greater than 25 The quotient of a number and 3 is no more than 15
SOLVING INEQUALITIES The solutions of an inequality are the numbers (values) that make it true. We solve inequalities the same way we solve equations Except:when we multiply or divide by a negative number, we reverse the inequality symbol Hint: when you solve, put the variable on the LEFT, this ensures that the arrow on the graph points the same way as the pointed end of the inequality symbol
SOLVE EACH INEQUALITY.GRAPH THE SOLUTION.2x > 8
SOLVE EACH INEQUALITY.GRAPH THE SOLUTION.12 − 2 y ≥ 38
SOLVE EACH INEQUALITY.GRAPH THE SOLUTION.5 ( x + 3) ≤ 55
SOLVE EACH INEQUALITY.GRAPH THE SOLUTION.−2 ( w + 4 ) + 9 < −13
NO SOLUTION OR ALL REALNUMBERS AS SOLUTIONS When solving inequalities, we can reach solutions that seem strange and require analysis. If we reach a false statement, there are no solutions, and the statement is never true If the variable(s) drop out and we have a true statement or we reach a point where one side is identical to the other, the statement is always true for all real numbers.
IS THE INEQUALITY ALWAYS,SOMETIMES, OR NEVERTRUE?3 ( x + 5 ) < 30
IS THE INEQUALITY ALWAYS,SOMETIMES, OR NEVERTRUE?−2 ( 3 x + 1) > −6 x + 7
IS THE INEQUALITY ALWAYS,SOMETIMES, OR NEVERTRUE?5 ( 2 x − 3) − 7 x ≤ 3 x + 8
COMPOUND INEQUALITIES A compound inequality is an inequality statement that joins two inequalities using the word and or the word or.
COMPOUND INEQUALITIES To solve a compound inequality containing and: Find all values of the variable that make both inequalities true
SOLVE THE COMPOUNDINEQUALITY. GRAPH THESOLUTION.7 < 2 x + 1 and 3 x ≤ 18
SOLVE THE COMPOUNDINEQUALITY. GRAPH THESOLUTION.3 < 2 x + 1 < 11 This is a collapsed “and inequality”
COMPOUND INEQUALITIES To solve a compound inequality containing or: Find all values of the variable that make at least one of the inequalities true.
SOLVE THE COMPOUNDINEQUALITY. GRAPH THESOLUTION.7 + k ≥ 6 or 8 + k < 3
SOLVE THE COMPOUNDINEQUALITY. GRAPH THESOLUTION.7 w + 3 > 11 or 4 w − 1 < −13