Absolute Value Equations Absolute Value Inequalities

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- - Value Equations and InequalitiesAbsolute Value EquationsAbsolute Value - - 20 33Distance is greater than is is less than is is greater than is less than definition, the equation |x|= 3 can be solved by finding real numbers at a distance of three units from 0. Two numbers satisfy this equation, 3 and 3. So the solution set is {}.3, 3 - - 3Properties of Absolute Value1. For 0, if and only if or .ba bab a b>== = 2. if and only if or .a bab a b=== For any positive number b:3. if and only if .a bbab< <<4. if and only if or .a ba b ab> < > - - 4Example 1SOLVING Absolute Value EQUATIONSSolve 312x =SolutionFor the given expression 5 3xto have Absolute Value 12, it must represent either 12 or 12 . This requires applying Property 1, with a= 5 3xand b= - - 5Example 1SOLVING Absolute Value EQUATIONSSolve 312x =Solution5 312x =5 312x =or5 312x = Property 137x =or317x = Subtract or173x=Divide by 3.

Absolute Value Equations and Inequalities. Absolute Value Equations. Absolute Value Inequalities. 1.8 - 2 –3. 0. 3. Distance is greater than 3. Distance is 3. Distance is less than 3. ... The absolute value of a number will be 0 only if that number is 0. Therefore, c. 5 15 0. x += 5 15 0 x

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