Section 1.6 Absolute Value Equations 101 5w 1, Answers 8. 9. e 4 5 , 2 f 1.26 5 Subtract 4.1 from both sides. p 4.1 p 4.1 p 4.1 Check: 0 4.1 p 0 6.9 6.9 4.1 4.1 0 6.9 6.9 00 0 6.9 6.9 0 54.16. 6.9 6.9 The solution set is ✔ Skill Practice Solve the equation. 8. 3.5 0 1.2 x 0 3.5 2. Solving Equations Containing Two Absolute Values 0x 0 0y 0 Some equations have two absolute values such as . If two quantities have the same absolute value, then the quantities are equal or the quantities are opposites. Solving an Equation Having Two Absolute Values Example 6 Solve the equation. Solution: Rewrite as two equations, Solve for w. 02w 3 0 05w 1 0 02w 3 0 05w 1 0 2w 3 5w 1 or 2w 3 5w 1 3w 3 1 or 7w 3 1 3w 4 or 7w 2 w 4 3 or w The solution set is e 4 3 , 2 7 f . Skill Practice Solve the equation. 9. 03 2x 0 03x 1 0 2 7 x y or x y. 2w 3 5w 1 or 2w 3 15w 12 Avoiding Mistakes To take the opposite of the quantity use parentheses and apply the distributive property. Both values check in the original equation. Equality of Absolute Values 0x 0 implies that x y or x y. 0 y 0
miller_intermediate_algebra_4e_ch1_3
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