Example: 2(8u + 2) = 3(2u 7) – 16u + 4 = 6u 21 – 16u + 4 6u = 6u 21 6u – – – 10u + 4 = –21 10u + 4 4 = 4 – –21 – 10u = –25 = = u –2.5 Exercises: 92. 2m + 12 = 3m 31 43 93. 7a 3 = 3 2a – – – 94. 4x 9 = 7x + 12 -7 95. 5 + 3r = 5r 19 12 – – 8q + 12 = 4(3 + 2q) 6(–3v + 1) = 5(–2v 2) 96. identity 97. 2 – 98. 3(8 3t) = 5(2 + 1 99. 8(2f 2) = 7(3f + 2) 6 t) – – 100. 6(w 1) = 3(3w + 5) -7 101. 6 = 6 6 v v – – – Lesson 2-5: Solving Equations Involving Absolute Values Absolute Value Equations When solving equations that involve absolute value, there are two cases to consider. Case 1: The value inside the absolute value symbols is positive. Case 2: The value inside the absolute value symbols is negative. Example 1: Solve + 4⎪ = 1. ⎪x Write + 4⎪ = 1 as + 4 = 1 or + 4 = x x –1. ⎪x + 4 = 1 or + 4 = x x –1 + 4 4 = 1 4 + 4 4 = 4 x x – – – –1 – = = x x –3 –5 Exercises: 102. + 1⎪ = 5 4,-6 103. + 2⎪ = 1 -1,-3 104. 2⎪ = 2 4,0 – ⎪w ⎪n ⎪w 105. 3⎪ = 1 4,2 106. + 6⎪ = 4 -2,-10 107. 5⎪ = 4 9,1 – – ⎪c ⎪t ⎪k
Example: 2(8u + 2) = 3(2u – 7) 16u + 4 = 6u – 21 16u + 4 – 6u = 6u – 21 – 6u 10u + 4 = –21 10u + 4 – 4 = –21 – 4 10u = –25 = u = –2.5 Exercises: 92. 2m + 12 = 3m – 31 43 93. 7a – 3 = 3 – 2a 94. 4x – 9 = 7x + 12 -7 95. 5 + 3r = 5r – 19 12 96. 8q + 12 = 4(3 + 2q) identity 97. 6(–3v + 1) = 5(–2v – 2) 2 98. 3(8 – 3t) = 5(2 + t) 1 99. 8(2f – 2) = 7(3f + 2) 6 100. 6(w – 1) = 3(3w + 5) -7 101. v – 6 = 6 – v 6 Lesson 2-5: Solving Equations Involving Absolute Values Absolute Value Equations When solving equations that involve absolute value, there are two cases to consider. Case 1: The value inside the absolute value symbols is positive. Case 2: The value inside the absolute value symbols is negative. Example 1: Solve ⎪x + 4⎪ = 1. Write ⎪x + 4⎪ = 1 as x + 4 = 1 or x + 4 = –1. x + 4 = 1 or x + 4 = –1 x + 4 – 4 = 1 – 4 x + 4 – 4 = –1 – 4 x = –3 x = –5 Exercises: 102. ⎪w + 1⎪ = 5 4,-6 103. ⎪n + 2⎪ = 1 -1,-3 104. ⎪w – 2⎪ = 2 4,0 105. ⎪c – 3⎪ = 1 4,2 106. ⎪t + 6⎪ = 4 -2,-10 107. ⎪k – 5⎪ = 4 9,1