Explanation Given Information: The provided inequality is 0.4 ( 2 x + 8 ) ≥ 20 − ( x + 5 ) . 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 0.4 ( 2 x + 8 ) ≥ 20 − ( x + 5 ) . Use distributive law and remove parentheses from the inequality 0.4 ( 2 x + 8 ) ≥ 20 − ( x + 5 ) , 0.8 x + 3.2 ≥ 20 − x − 5 0.8 x + 3.2 ≥ 15 − x Use multiplication principle, multiply by 10 on both sides of the inequality 0.8 x + 3.2 ≥ 15 − x to remove the decimal. 10 ( 0.8 x + 3

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Chapter 8.7, Problem 82ES

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To calculate: The solutions of the inequality 0.4(2x+8)≥20−(x+5) using the addition principle and the multiplication principle.

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Chapter 8.7, Problem 81ES

Chapter 8.7, Problem 83ES

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Ch. 8.1 - Objective 7.1a: Evaluate algebraic expressions by...Ch. 8.1 - Prob. 2SR Ch. 8.1 - Prob. 1DE Ch. 8.1 - Prob. 2DE Ch. 8.1 - Prob. 3DE Ch. 8.1 - Prob. 4DE Ch. 8.1 - Prob. 5DE Ch. 8.1 - Prob. 6DE Ch. 8.1 - Prob. 7DE Ch. 8.1 - Prob. 8DE

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The solutions of the inequality 0.4 ( 2 x + 8 ) ≥ 20 − ( x + 5 ) using the addition principle and the multiplication principle.

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

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To calculate: The solutions of the inequality 0.4(2x+8)≥20−(x+5) using the addition principle and the multiplication principle.

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