Definition of absolute valueDefinition of absolute value: the absolute value of a number is the distance the number is from zero Look at the following two graphs: The first one shows 6 located at a distance of 6 units from zero. We write 6 = 6 The second one shows 8 located at a distance of 8 units from zero. We write 8 = 8 You can see from this that the absolute value of a number is always positive with the exception of taking the absolute value of 0 (0 = 0) Therefore, do not write 5 = 5 or 4 = 4 please! 6 means distance from 0 to 6 8 means distance from 0 to 8 For 8 = 8, you could also argue that to get 8, you have to take the negative of 8 since   8 = 8 So,   8 =   8 = 8 This observation helps us to come up with a formal definition of absolute value  x  = x if x is positive or zero, but x if x is negative This definition is important to understand before solving absolute value equations or absolute value inequalities Calculate the absolute value of the following numerical expressions 1) 4^{2} − 4 × 2 2) 5 + 5 × 2 − 15 3) 8 + 2 × 5 1)  8 + 2 × 5  =  8 + 10   8 + 2 × 5  =  2   8 + 2 × 5  = 2 2)  4^{2} − 4 × 2 =  16 − 4 × 2  4^{2} − 4 × 2 =  16 − 8  4^{2} − 4 × 2 =  8   4^{2} − 4 × 2 = 8 3) 5 + 5 × 2 − 15 =  5 + 10 − 15  (5 + 5 × 2 − 15) =  5 − 15  (5 + 5 × 2 − 15) =  15  (5 + 5 × 2 − 15) = 15 Related topics Solving absolute value equations Solving absolute value inequalities 




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