10 Chapter 1 Real Numbers and Algebraic Expressions Objective 5 Examples Simplify each absolute value expression. Problems Solutions 5a. u4 u Because 4 is 4 units from 0 on a number line, u4 u = 4. 5b. u0 u Because 0 is 0 units from 0 on a number line, u0 u = 0. 5c. `- 2 5 ` Because - 2 5 is 2 5 units from 0 on a number line, `- 2 5 ` = 2 5 . 5d. -u8 u We need to find the opposite of the absolute value of 8. The absolute value of 8 is 8. Its opposite is -8. So, -u8u = -(8)=-8 5e. -u-5 u We need to find the opposite of the absolute value of -5. The absolute value of -5 is 5. Its opposite is -5. So, -u-5u = -(5)=-5 Student Check 5 Simplify each absolute value expression. a. u12 u b. u 13 u c. P- 3 5 P d. -u1 u e. -u-1 u Troubleshooting Common Errors Some common errors associated with the classification of real numbers and finding absolute values are shown. Objective 6 Examples A problem and an incorrect solution are given. Provide the correct solution and an explanation of the error. 6a. Determine if 181 is a natural number, whole number, integer, rational number or irrational number. Incorrect Solution Correct Solution and Explanation 181 is an irrational number since 181 = 9 since 9 · 9 = 81. Therefore, it involves ves a square root sy symbol. 181 is a natural number, whole number, integer, and rational number. 6b. Simplify -u-3 u. nu Incorrect Solution Correct Solution and Explanation This expression means to find the opposite -u-3 u = 3 of the absolute value of -3. Since u-3 u = 3, its opposite is -3. u -u-3 u = -(3) = -3 Objective 6 ▶ Troubleshoot common errors.
hendricks_intermediate_algebra_1e_ch1_3
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