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Solving Absolute Value Equations,[object Object],Goals:  ,[object Object],Solve equations involving absolute values,[object Object],Rewrite absolute value inequalities in compound form and solve,[object Object]
Definition,[object Object],The absolute value of a number, x, is the distance the number is from 0.,[object Object],Since distance is nonnegative, the absolute value of a number is always nonnegative.,[object Object],x,[object Object],, if x is positive,[object Object]
Definition,[object Object],The absolute value of a number, x, is the distance the number is from 0.,[object Object],Since distance is nonnegative, the absolute value of a number is always nonnegative.,[object Object],x,[object Object],, if x is positive,[object Object],0,[object Object],, if x is 0,[object Object]
Definition,[object Object],The absolute value of a number, x, is the distance the number is from 0.,[object Object],Since distance is nonnegative, the absolute value of a number is always nonnegative.,[object Object],x,[object Object],, if x is positive,[object Object],0,[object Object],, if x is 0,[object Object],-x,[object Object],, if x is negative,[object Object]
If you take the negative of an absolute value,,[object Object],Then your answer becomes negative.,[object Object],!!!CAUTION!!!,[object Object]
, then the x can be equal ,[object Object],If the,[object Object],to either 6 or -6.,[object Object],Therefore, when taking the absolute value of an equation, there are TWO possible solutions:,[object Object],OR,[object Object],Absolute Value Equations,[object Object]
Now solve both equations separately:,[object Object],Write your solutions together:,[object Object],x = -7 or 3,[object Object],Absolute Value Equations,[object Object]
EXAMPLES:,[object Object],1),[object Object],2),[object Object],3),[object Object],4),[object Object]
EXAMPLES:,[object Object],1),[object Object],2),[object Object],3),[object Object],4),[object Object],x = -2 or 8,[object Object]
EXAMPLES:,[object Object],1),[object Object],2),[object Object],3),[object Object],4),[object Object],x = -2 or 8,[object Object],x = -6 or 1,[object Object]
EXAMPLES:,[object Object],1),[object Object],2),[object Object],3),[object Object],4),[object Object],x = -2 or 8,[object Object],x = -6 or 1,[object Object],x = -10 or -6,[object Object]
EXAMPLES:,[object Object],1),[object Object],2),[object Object],3),[object Object],4),[object Object],x = -2 or 8,[object Object],x = -6 or 1,[object Object],x = -10 or -6,[object Object],-11,[object Object],  2,[object Object],x = -4 or,[object Object]
The way to solve multi-step absolute value equations is like solving a multi-step linear equation.,[object Object],Instead of solving by isolating the variable by undoing,[object Object],     1st:  addition/subtraction,[object Object],     2nd:  multiplication/division,[object Object],You isolate the absolute value by undoing,[object Object],     1st:   addition/subtraction outside the abs. value,[object Object],     2nd:  multiplication/division outside the abs. value,[object Object],Multi-Step Absolute Value Equations,[object Object]
Walk-Through:  Solve the following,[object Object], -7,[object Object],  3,[object Object],x = 3 or,[object Object]
x = -12 or -2,[object Object],Walk-Through:  Solve the following,[object Object]
Solve the following absolute value equations:,[object Object],1),[object Object],2),[object Object],3),[object Object],Try the Following On Your Own:,[object Object]
Solve the following:,[object Object],1),[object Object],x =       or 4,[object Object],2),[object Object],3),[object Object], -2,[object Object],  3,[object Object],Solutions:,[object Object]
Solve the following:,[object Object],1),[object Object],x =       or 4,[object Object],2),[object Object],x =      or  ,[object Object],3),[object Object], -2,[object Object],  3,[object Object], -9,[object Object],  2,[object Object], 19,[object Object],  2,[object Object],Solutions:,[object Object]
Solve the following:,[object Object],1),[object Object],x =       or 4,[object Object],2),[object Object],x = -1 or 6,[object Object],3),[object Object],x = -6 or 0,[object Object], -2,[object Object],  3,[object Object],Solutions:,[object Object]

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