Explanation Given Information: The provided inequality is 5 ( x + 3 ) + 9 ≤ 3 ( x − 2 ) + 6 . Formula used: The Addition Principle for inequalities: For any real numbers a, b, and c , The inequality a < b is equivalent to a + c < b + c . The inequality a > b is equivalent to a + c > b + c . The inequality a ≤ b is equivalent to a + c ≤ b + c . The inequality a ≥ b is equivalent to a + c ≥ b + c . The Multiplication Principle for inequalities: For any real numbers a, b, and any positive number c , The inequality a < b is equivalent to a c < b c . The inequality a > b is equivalent to a c > b c . For any real numbers a, b, and any negative number c , The inequality a < b is equivalent to a c > b c . The inequality a > b is equivalent to a c < b c . The similar statements hold for ≤ and ≥ . The Distributive law, a ( b + c ) = a b + a c Calculation: The provided inequality is 5 ( x + 3 ) + 9 ≤ 3 ( x − 2 ) + 6 . Use distributive law and remove parentheses from the inequality 5 ( x + 3 ) + 9 ≤ 3 ( x − 2 ) + 6 , 5 x + 15 + 9 ≤ 3 x − 6 + 6 5 x + 24 ≤ 3 x Use the addition principle, subtract 24 from both sides of the inequality

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ISBN: 9780321997173

Author: Marvin L. Bittinger, Judith A. Beecher

Publisher: PEARSON

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Chapter 8.7, Problem 80ES

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To calculate: The solutions of the inequality 5(x+3)+9≤3(x−2)+6 using the addition principle and the multiplication principle.

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Chapter 8.7, Problem 79ES

Chapter 8.7, Problem 81ES

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The solutions of the inequality 5 ( x + 3 ) + 9 ≤ 3 ( x − 2 ) + 6 using the addition principle and the multiplication principle.

Solution Summary: The author calculates the solutions of the inequality using the addition principle and the multiplication principle.

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To calculate: The solutions of the inequality 5(x+3)+9≤3(x−2)+6 using the addition principle and the multiplication principle.

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Chapter 8 Solutions