Explanation Given Information: The provided equation is t + 4 = 1 − 3 t + 1 . Formula used: The principle of squaring, if a = b , then, a 2 = b 2 The square of the binomial is the square of the first term, plus twice the product of the two terms, plus the square of the last term, ( A − B ) 2 = A 2 − 2 A B + B 2 , where any real number A is the first term and any real number B is the last term. The principle of zero products is for any real numbers A and B , if A B = 0 then A = 0 or B = 0 . Calculation: Consider the equation, t + 4 = 1 − 3 t + 1 ………… (1) Apply the principle of squaring, and, square both sides, ( t + 4 ) 2 = ( 1 − 3 t + 1 ) 2 t + 4 = ( 1 − 3 t + 1 ) 2 Recall that the square of the binomial is the square of the first term, plus twice the product of the two terms, plus the square of the last term, ( A − B ) 2 = A 2 − 2 A B + B 2 , where any real number A is the first term and any real number B is the last term. Substitute 1 for A and 3 t + 1 for B in ( A − B ) 2 = A 2 − 2 A B + B 2 and solve t + 4 = ( 1 − 3 t + 1 ) 2 . t + 4 = ( 1 ) 2 − 2 ( 1 ) ( 3 t + 1 ) + ( 3 t + 1 ) 2 t + 4 = 1 − 2 3 t + 1 + 3 t + 1 t + 4 = 2 − 2 3 t + 1 + 3 t Combine the like terms together and isolate the radical. t + 4 = 2 − 2 3 t + 1 + 3 t t − 3 t + 4 − 2 = − 2 3 t + 1 − 2 t + 2 = − 2 3 t + 1 − 2 ( t − 1 ) = − 2 3 t + 1 Divide from both sides by − 2 , − 2 ( t − 1 ) − 2 = − 2 <

Elementary Algebra: Concepts and Applications (10th Edition)

10th Edition

ISBN: 9780134441375

Author: Marvin L. Bittinger, David J. Ellenbogen, Barbara L. Johnson

Publisher: PEARSON

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Chapter 8.5, Problem 65ES

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To calculate: The solution of the equation t+4=1−3t+1.

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Chapter 8.5, Problem 64ES

Chapter 8.5, Problem 66ES

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Chapter 8 Solutions

Elementary Algebra: Concepts and Applications (10th Edition)

Ch. 8.1 - Find the square roots of 81.Ch. 8.1 - Prob. 2YT Ch. 8.1 - Prob. 3YT Ch. 8.1 - Prob. 4YT Ch. 8.1 - Prob. 5YT Ch. 8.1 - Prob. 6YT Ch. 8.1 - Prob. 7YT Ch. 8.1 - Prob. 8YT Ch. 8.1 - Prob. 1CYU Ch. 8.1 - Prob. 2CYU

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The solution of the equation t + 4 = 1 − 3 t + 1 .

Solution Summary: The author calculates the solution of the equation, sqrtt+4=1-

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To calculate: The solution of the equation t+4=1−3t+1.

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Chapter 8 Solutions