Explanation Given information: The provided equation is x + 4 = 4 x + 1 . Formula used: Principle of squaring states that if two numbers, a and b are equal, their squares are equal as well. Mathematically, If a = b then a 2 = b 2 Follow the steps to solve the problem: Step1: Isolate one of the radical terms on one side of the equation. Step2: Apply the principle of squaring. Step3: Perform steps 1 and 2 again if there remains a radical expression in the equation. Step4: Solve the equation. Step5: Verify the solutions obtained. The following expansion formula is used: ( a − b ) 2 = a 2 − 2 a b + b 2 In such type of questions, factorize the given polynomial and then apply the principle of zeroes. Principle of zeroes states that if the product of two or more expressions is 0 then either one or two or all of them are 0 . Calculation: Consider the equation, x + 4 = 4 x + 1 Apply the principle of squares and expand using the quadratic expansion, ( x + 4 ) 2 = ( 4 x + 1 ) 2 x 2 + 8 x + 16 = 16 ( x + 1 ) x 2 + 8 x + 16 = 16 x + 16 Subtract 16 x + 16 from both the sides,

9th Edition

ISBN: 9780321997173

Author: Marvin L. Bittinger, Judith A. Beecher

Publisher: PEARSON

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Chapter 14.5, Problem 24ES

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To calculate: The value of x for the equation x+4=4x+1.

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Chapter 14.5, Problem 23ES

Chapter 14.5, Problem 25ES

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Chapter 14 Solutions

Developmental Mathematics (9th Edition)

Ch. 14.1 - Prob. 1SR Ch. 14.1 - Prob. 2SR Ch. 14.1 - Prob. 1DE Ch. 14.1 - Prob. 2DE Ch. 14.1 - Prob. 3DE Ch. 14.1 - Prob. 4DE Ch. 14.1 - Prob. 5DE Ch. 14.1 - Prob. 6DE Ch. 14.1 - Prob. 7DE Ch. 14.1 - Prob. 8DE

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The value of x for the equation x + 4 = 4 x + 1 .

Solution Summary: The author explains the principle of squaring, which states that if two numbers, a-b- are equal, their squares are equally.

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To calculate: The value of x for the equation x+4=4x+1.

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Chapter 14 Solutions