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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 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, 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) 42 − 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) | 42 − 4 × 2| = | 16 − 4 × 2| | 42 − 4 × 2| = | 16 − 8| | 42 − 4 × 2| = | 8 | | 42 − 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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