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 




Are you a fan of this site? Support us Our awards! Our partners About me Disclaimer Build your website! Advertise on my site Try our free toolbar Like us on Facebook Take our survey 

