Explanation Given Information: The inequality is, 0.8 − 4 ( b − 1 ) > 0.2 + 3 ( 4 − b ) . Formula used: Solve the linear inequalities as, Step 1. Simplify the terms on each side of the equation by clearing parenthesis, fractions, decimals and by combining the like terms. Step 2. Resolve all the variable terms on one side of the equation and the constants on the other side of the equation. Step 3. Solve for the variable, that is, write the equation with the variable on one side of the equation and the constant representing the value of the variable on the other side of the equation. The distributive property for any number a , b and c is given by, a ( b + c ) = a b + a c Calculation: Consider the inequality, 0.8 − 4 ( b − 1 ) > 0.2 + 3 ( 4 − b ) Use distributive property to clear the fractions in the above inequality as, 0.8 − 4 ⋅ b + 4 ⋅ 1 > 0.2 + 3 ⋅ 4 − 3 ⋅ b 0.8 − 4 b + 4 > 0.2 + 12 − 3 b 4.8 − 4 b > 12.2 − 3 b Next, add 3 b and subtract 4.8 from each side of the above inequality as 4.8 − 4 b + 3 b − 4.8 > 12.2 − 3 b + 3 b − 4.8 − b > 7.4 Next, divide each side of the above inequality by − 1 and reverse the inequality symbol as division is by negative integer, − b − 1 > 7.4 − 1 b < − 7.4 Check that any value of b greater than − 7.4 that would not satisfy the inequality, while any value less than − 7.4 would satisfy the inequality. Thus, substitute 0 for x in the inequality 0.8 − 4 ( b − 1 ) > 0.2 + 3 ( 4 − b ) and solve as, 0.8 − 4 ( ( 0 ) − 1 ) > ? 0.2 + 3 ( 4 − ( 0 ) ) 0

13th Edition

ISBN: 8220106960332

Author: Johnson

Publisher: PEARSON

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Chapter 1.4, Problem 70ES

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To calculate: The solution set for the inequality, 0.8−4(b−1)>0.2+3(4−b).

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Chapter 1.4, Problem 69ES

Chapter 1.4, Problem 71ES

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EBK INTERMEDIATE ALGEBRA

Ch. 1.1 - a. b. c. d. e. f. 1. Which equations are...Ch. 1.1 - a. 3+4=7 b. 51=2 c. 21+2=24 d. x5=12 e. 9x=x f....Ch. 1.1 - a. 3+4=7 b. 51=2 c. 21+2=24 d. x5=12 e. 9x=x f....Ch. 1.1 - Determine whether the given number is a solution...Ch. 1.1 - Determine whether the given number is a solution...Ch. 1.1 - Determine whether the given number is a solution...Ch. 1.1 - 7. Determine whether are equivalent. Ch. 1.1 - 8. Determine whether are equivalent. Ch. 1.1 - Solve using the addition principle. x+9=2 Ch. 1.1 - Solve using the addition principle. x+14=35

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