Section 1.1 Sets and the Real Numbers 9 Objective 4 Examples Find the opposite of each number. Problems Solutions 4a. -4 -(-4) = 4 4b. 20 -(20) = -20 4c. 7 8 -a7 8 b = - 7 8 4d. -5 1 3 -a-5 1 3 b = 5 1 3 4e. 17 -(17) = -17 4f. -π -(-π) = π Student Check 4 Find the opposite of each number. a. 10 b. -14 c. - 1 2 d. 25 6 e. -16 f. 8.2 Absolute Value The absolute value of a number refers to the number’s distance from zero on a real number line. –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 3 units 3 units The numbers -3 and 3 are both 3 units from 0 on the real number line, so the absolute value of these numbers is 3. We use vertical bars to denote the absolute value of a number a, uau. Since absolute value refers to distance, the absolute value of a number is always greater than or equal to zero. Verbal Statement Mathematical Statement The absolute value of 3 is 3. u3u = 3 The absolute value of -3 is 3. u-3u = 3 Definition: The absolute value of a real number a, denoted uau, is the distance between a and 0 on the real number line. If a ≥ 0, uau = a. If a < 0, uau =-a. Note: The absolute value of a number that is positive or zero is that number. The absolute value of a negative number is its opposite. Objective 5 ▶ Find the absolute value of a real number.
hendricks_intermediate_algebra_1e_ch1_3
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