Explanation Result used: Addition principle: For any a , b , and c , if a < b is true, then a + c < b + c is true. Multiplication principle: a) If a < b and c > 0 are true, then a c < b c is true. b) If a < b and c < 0 are true, then a c > b c is true. When a negative number multiplies both sides of an inequality, then the inequality symbol gets reversed. Calculation: The given inequality is 8 − 2 w ≤ − 14 . Use the multiplication principle and solve the inequality as follows. 8 − 2 w ≤ − 14 8 − 2 w − 8 ≤ − 14 − 8

College Algebra: Graphs and Models (6th Edition)

6th Edition

ISBN: 9780134179032

Author: Marvin L. Bittinger, Judith A. Beecher, David J. Ellenbogen, Judith A. Penna

Publisher: PEARSON

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Chapter J.18, Problem 6E

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To solve: The inequality 8−2w≤−14.

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Chapter J.18, Problem 5E

Chapter J.19, Problem 1E

Chapter J Solutions

College Algebra: Graphs and Models (6th Edition)

Ch. J.1 - In Exercises 1-6, consider the numbers 23, 6, 3,...Ch. J.1 - In Exercises 16, consider the numbers 23, 6, 3,...Ch. J.1 - In Exercises 16, consider the numbers 23, 6, 3,...Ch. J.1 - In exercises 16, consider the numbers 23, 6, 3,...Ch. J.1 - In Exercises 16, consider the numbers 23, 6, 3,...Ch. J.1 - In Exercises 16, consider the numbers 23, 6, 3,...Ch. J.2 - Name the property illustrated by the sentence. 1....Ch. J.2 - Name the property illustrated by the sentence. 2....Ch. J.2 - Name the property illustrated by the sentence. 3....Ch. J.2 - Prob. 4E

Ch. J.2 - Prob. 5E Ch. J.2 - Prob. 6E Ch. J.2 - Prob. 7E Ch. J.2 - Prob. 8E Ch. J.2 - Prob. 9E Ch. J.2 - Prob. 10E Ch. J.3 - Classify the inequality as true or false. 1. 9 9 Ch. J.3 - Prob. 2E Ch. J.3 - Classify the inequality as true or false. 3. 265 Ch. J.3 - Prob. 4E Ch. J.3 - Prob. 5E Ch. J.3 - Prob. 6E Ch. J.4 - Simplify. 1. |98|Ch. J.4 - Prob. 2E Ch. J.4 - Prob. 3E Ch. J.4 - Prob. 4E Ch. J.4 - Prob. 5E Ch. J.4 - Prob. 6E Ch. J.4 - Prob. 7E Ch. J.4 - Prob. 8E Ch. J.5 - Compute and simplify. 1. 8 (11)Ch. J.5 - Compute and simplify. 2. 310(13)Ch. J.5 - Prob. 3E Ch. J.5 - Prob. 4E Ch. J.5 - Prob. 5E Ch. J.5 - Prob. 6E Ch. J.5 - Prob. 7E Ch. J.5 - Prob. 8E Ch. J.5 - Prob. 9E Ch. J.5 - Prob. 10E Ch. J.5 - Prob. 11E Ch. J.5 - Compute and simplify. 12. 1223 Ch. J.5 - Prob. 13E Ch. J.5 - Prob. 14E Ch. J.5 - Prob. 15E Ch. J.6 - Write interval notation. 1. {x| 5 x 5}Ch. J.6 - Prob. 2E Ch. J.6 - Write interval notation. 3. {x | x 2}Ch. J.6 - Write interval notation. 4. {x | x 3.8}Ch. J.6 - Prob. 5E Ch. J.6 - Prob. 6E Ch. J.6 - Prob. 7E Ch. J.6 - Prob. 8E Ch. J.6 - Prob. 9E Ch. J.6 - Write interval notation for the graph. 10.Ch. J.7 - Simplify. 1. 36 Ch. J.7 - Prob. 2E Ch. J.7 - Prob. 3E Ch. J.7 - Prob. 4E Ch. J.7 - Prob. 5E Ch. J.7 - Prob. 6E Ch. J.7 - Prob. 7E Ch. J.7 - Prob. 8E Ch. J.7 - Prob. 9E Ch. J.7 - Prob. 10E Ch. J.8 - Convert to scientific notation. 1. 18,500,000 Ch. J.8 - Prob. 2E Ch. J.8 - Prob. 3E Ch. J.8 - Prob. 4E Ch. J.8 - Convert to decimal notation. 5.4.3 108 Ch. J.8 - Prob. 6E Ch. J.8 - Convert to decimal notation. 7.6.203 1011 Ch. J.8 - Prob. 8E Ch. J.9 - Calculate. 1. 3 + 18 6 3 Ch. J.9 - Calculate. 2. 5 3 + 8 32 + 4(6 2)Ch. J.9 - Calculate. 3. 5(3 8 32 + 4 6 2)Ch. J.9 - Calculate. 4. 16 4 4 2 256 Ch. J.9 - Calculate. 5. 26 23 210 28 Ch. J.9 - Calculate. 6. 4(86)243+2831+190 Ch. J.9 - Calculate. 7. 64 [(4) (2)]Ch. J.9 - Prob. 8E Ch. J.10 - Determine the degree of the polynomial. 1. 5 x6 Ch. J.10 - Prob. 2E Ch. J.10 - Prob. 3E Ch. J.10 - Prob. 4E Ch. J.10 - Prob. 5E Ch. J.10 - Prob. 6E Ch. J.10 - Prob. 7E Ch. J.10 - Prob. 8E Ch. J.11 - Add or subtract. 1. (8y 1) (3 y)Ch. J.11 - Add or subtract. 2. (3x2 2x x3 + 2) (5x2 8x ...Ch. J.11 - Prob. 3E Ch. J.11 - Prob. 4E Ch. J.11 - Prob. 5E Ch. J.12 - Prob. 1E Ch. J.12 - Prob. 2E Ch. J.12 - Prob. 3E Ch. J.12 - Prob. 4E Ch. J.12 - Prob. 5E Ch. J.12 - Prob. 6E Ch. J.13 - Multiply. 1. (x + 3)2 Ch. J.13 - Multiply. 2. (5x 3)2 Ch. J.13 - Multiply. 3. (2x + 3y)2 Ch. J.13 - Prob. 4E Ch. J.13 - Multiply. 5. (n + 6) (n 6)Ch. J.13 - Prob. 6E Ch. J.14 - Factor out the largest common factor. 1. 3x + 18 Ch. J.14 - Prob. 2E Ch. J.14 - Prob. 3E Ch. J.14 - Prob. 4E Ch. J.14 - Prob. 5E Ch. J.14 - Prob. 6E Ch. J.14 - Prob. 7E Ch. J.14 - Prob. 8E Ch. J.14 - Prob. 9E Ch. J.14 - Prob. 10E Ch. J.14 - Prob. 11E Ch. J.14 - Prob. 12E Ch. J.15 - Factor. 1. 8x2 6x 9 Ch. J.15 - Factor. 2. 10t2 + 4t 6 Ch. J.15 - Factor. 3. 18a2 51a + 15 Ch. J.16 - Factor the difference of squares. 1. z2 81 Ch. J.16 - Factor the difference of squares. 2. 16x2 9 Ch. J.16 - Factor the difference of squares. 3. 7pq4 7py4 Ch. J.16 - Factor the square of a binomial. 4. x2 + 12x + 36 Ch. J.16 - Prob. 5E Ch. J.16 - Factor the square of a binomial. 6. a3 + 24a2 +...Ch. J.16 - Factor the sum or the difference of cubes. 7. x3 +...Ch. J.16 - Factor the sum or the difference of cubes. 8. m3 ...Ch. J.16 - Prob. 9E Ch. J.16 - Prob. 10E Ch. J.17 - Prob. 1E Ch. J.17 - Prob. 2E Ch. J.17 - Prob. 3E Ch. J.17 - Prob. 4E Ch. J.17 - Solve. 5. 7y 1 = 23 5y Ch. J.17 - Prob. 6E Ch. J.17 - Prob. 7E Ch. J.17 - Solve. 8. 5y 4 (2y 10) = 25 Ch. J.18 - Prob. 1E Ch. J.18 - Prob. 2E Ch. J.18 - Prob. 3E Ch. J.18 - Prob. 4E Ch. J.18 - Prob. 5E Ch. J.18 - Prob. 6E Ch. J.19 - Prob. 1E Ch. J.19 - Prob. 2E Ch. J.19 - Prob. 3E Ch. J.19 - Prob. 4E Ch. J.19 - Prob. 5E Ch. J.19 - Prob. 6E Ch. J.19 - Prob. 7E Ch. J.19 - Prob. 8E Ch. J.20 - Prob. 1E Ch. J.20 - Prob. 2E Ch. J.20 - Prob. 3E Ch. J.20 - Prob. 4E Ch. J.20 - Prob. 5E Ch. J.20 - Prob. 6E Ch. J.21 - Prob. 1E Ch. J.21 - Prob. 2E Ch. J.21 - Prob. 3E Ch. J.21 - Prob. 4E Ch. J.21 - Prob. 5E Ch. J.21 - Prob. 6E Ch. J.22 - Prob. 1E Ch. J.22 - Prob. 2E Ch. J.22 - Prob. 3E Ch. J.22 - Prob. 4E Ch. J.22 - Prob. 5E Ch. J.22 - Prob. 6E Ch. J.23 - Prob. 1E Ch. J.23 - Prob. 2E Ch. J.23 - Prob. 3E Ch. J.23 - Prob. 4E Ch. J.23 - Prob. 5E Ch. J.23 - Prob. 6E Ch. J.24 - Simplify. 1. xyyx1y+1x Ch. J.24 - Prob. 2E Ch. J.24 - Prob. 3E Ch. J.24 - Prob. 4E Ch. J.24 - Simplify. 5. abba1a1b Note: b a = 1(a b)Ch. J.25 - Prob. 1E Ch. J.25 - Prob. 2E Ch. J.25 - Prob. 3E Ch. J.25 - Prob. 4E Ch. J.25 - Prob. 5E Ch. J.25 - Prob. 6E Ch. J.25 - Prob. 7E Ch. J.25 - Prob. 8E Ch. J.25 - Prob. 9E Ch. J.25 - Prob. 10E Ch. J.25 - Prob. 11E Ch. J.25 - Prob. 12E Ch. J.25 - Prob. 13E Ch. J.25 - Prob. 14E Ch. J.25 - Prob. 15E Ch. J.25 - Prob. 16E Ch. J.25 - Prob. 17E Ch. J.25 - Prob. 18E Ch. J.25 - Prob. 19E Ch. J.25 - Prob. 20E Ch. J.26 - Prob. 1E Ch. J.26 - Prob. 2E Ch. J.26 - Prob. 3E Ch. J.26 - Prob. 4E Ch. J.26 - Prob. 5E Ch. J.26 - Prob. 6E Ch. J.26 - Prob. 7E Ch. J.26 - Prob. 8E Ch. J.27 - Prob. 1E Ch. J.27 - Prob. 2E Ch. J.27 - Prob. 3E Ch. J.27 - Prob. 4E Ch. J.27 - Prob. 5E Ch. J.27 - Prob. 6E Ch. J.27 - Prob. 7E Ch. J.27 - Convert to exponential notation. 8. x5 Ch. J.27 - Prob. 9E Ch. J.27 - Prob. 10E Ch. J.27 - Prob. 11E Ch. J.28 - Find the length of the third side of each right...Ch. J.28 - Find the length of the third side of each right...Ch. J.28 - Find the length of the third side of each right...Ch. J.28 - Find the length of the third side of each right...Ch. J.28 - Find the length of the third side of each right...

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The inequality 8 − 2 w ≤ − 14 .

Solution Summary: The author explains how to solve the inequality 8-2wle -14 using the multiplication principle.

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Chapter J Solutions