To determine The incorrect step in the sequence a < b , a b < b 2 , a b − b 2 < 0 , b ( a − b ) < 0 , b < 0. Explanation Property used: 1. Addition or subtraction of same number to each member of the inequality will not change the sense of the inequality. The property is symbolically denoted as, “if a < b then a + c < b + c and a − c < b − c .” 2. Multiplication or division of each member of the inequality by same positive number will not change the sense of the inequality. The property is symbolically denoted as, “if a < b then a c < b c and a c < b c where c > 0 .” 3. Multiplication or division of each member of the inequality by same negative number will reverse the sign of the inequality. The property is symbolically denoted as, “if a < b then a c > b c and a c > b c where c < 0 .” Calculation: The given inequality is 0 < a < b , which implies a and b are positive numbers. By property 1, the sense of the inequality 0 < a < b remains unchanged when b is subtracted from each member of the inequality. Subtract b from each member of the inequality 0 < a < b as shown below. 0 − b < a − b < b − b − b < a − b < 0 The above inequality − b < a − b < 0 implies that a − b is negative. Consider the first inequality a < b in the sequence. By property 2, the sense of the inequality a < b remains unchanged, when both members of the inequality are multiplied by b

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Author: Washington

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Chapter 17.1, Problem 48E

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The incorrect step in the sequence a<b, ab<b2, ab−b2<0, b(a−b)<0, b<0.

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Chapter 17.1, Problem 47E

Chapter 17.1, Problem 49E

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The incorrect step in the sequence a < b , a b < b 2 , a b − b 2 < 0 , b ( a − b ) < 0 , b < 0.