Explanation Given Information: The provided inequality is 3 ( 2 − 5 x ) + 2 x < 2 ( 4 + 2 x ) . Formula used: Solve the linear inequalities as, Step 1. Simplify the terms on each side of the equation by clearing parenthesis, fractions and decimals 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, 3 ( 2 − 5 x ) + 2 x < 2 ( 4 + 2 x ) Use distributive property to clear parenthesis in the expression to simplify the inequality as, 3 ⋅ 2 − 3 ⋅ 5 x + 2 x < 2 ⋅ 4 + 2 ⋅ 2 x 6 − 15 x + 2 x < 8 + 4 x 6 − 13 x < 8 + 4 x Add 13 x and subtract 8 from each side of the above inequality as 6 − 13 x + 13 x − 8 < 8 + 4 x + 13 x − 8 − 2 < 17 x Now, divide each side of the above inequality by 17 to get, − 2 17 < 17 x 17 − 2 17 < x Implies, x > − 2 17 or − 0.12 Check that any value of x less than − 0.12 that would not satisfy the inequality, while any value greater than − 0.12 would satisfy the inequality

12th Edition

ISBN: 9780321924711

Author: Marvin L. Bittinger

Publisher: PEARSON

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Chapter 1.4, Problem 49ES

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To calculate: The solution set for the inequality 3(2−5x)+2x<2(4+2x).

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Chapter 1.4, Problem 48ES

Chapter 1.4, Problem 50ES

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Chapter 1 Solutions

Intermediate Algebra (12th Edition)

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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