Find (a) the opposite (or additive inverse) of the number and (b) the absolute value of th...

Find (a) the opposite (or additive inverse) of the number and (b) the absolute value of the number. See Objective and Example.

Find the additive inverse of a real number. By a property of the real numbers, for any real number x (except 0), there is exactly one number on the number line the same distance from 0 as x, but on the opposite side of 0. See figure. Such pairs of numbers are called additive inverses, or opposites, of each other.

FIGURE

EXAMPLE Finding the Absolute Value

Simplify by finding the absolute value.

(a) |0| = 0

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(b) |5| = 5

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(c) |−5| = −(−5) = 5

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(d) −|5| = −(5) = −5

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(e) −|−5| = −(5) = −5

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(f) |8 − 2| = |6| = 6

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(g) −|8 −2| = −|6| = −6

Parts (f) and (g) show that absolute value bars are grouping symbols. We perform any operations inside absolute value symbols before finding the absolute value.