Algebra: Structure And Method, Book 1
Algebra: Structure And Method, Book 1
(REV)00 Edition
ISBN: 9780395977224
Author: Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher: McDougal Littell
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Concept explainers

Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
Linear Functions
A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
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Question
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Chapter 5.6, Problem 61WE
To determine

To find : the solution of the equation

Expert Solution & Answer
Check Mark

Answer to Problem 61WE

The solution of the equation is x=−2

Explanation of Solution

Given information : (x+2)2−(x−2)2=(x−1)2−(x−3)2

Concept Involved:

Solve the equation by getting the variable in one side of the equation and undoing whatever is done to it by performing reverse operation. The solution to the equation is the value of x that makes the equation TRUE.

Formula Used:

  (p+q)2=p2+2pq+q2

  (p−q)2=p2−2pq+q2

Calculation:

Used the algebraic identity (p+q)2=p2+2pq+q2 & (p−q)2=p2−2pq+q2 to rewrite and expand the equation

  x2+2(x)(2)+22+x2−2(x)(2)+22=x2−2(x)(1)+12−(x2−2(x)(3)+32)

Simplify on both sides of the equation

  x2+4x+4−(x2−4x+4)=x2−2x+1−(x2−6x+9)

Distribute the negative and drop the parenthesis in both sides of the equation

  x2+4x+4−x2+4x−4=x2−2x+1−(x2−6x+9)

Group like terms in left side of the equation

  x2−x2+4x+4x+4−4=x2−x2−2x+6x+1−9

Combine like terms in left side of the equation

  8x=4x−8

In the process of getting x alone in one side of the equation we need to subtract 4x on both sides of the equation

  8x−4x=4x−8−4x

Group and combine the like terms on both sides of the equation

  4x=−8

Divide 4 on both sides of the equation

  4x4=−84

Simplify fraction on both sides of the equation

  x=−2

Check whether 6 substituted for x in original equation makes it TRUE.

  (−2+2)2−(−2−2)2=(−2−1)2−(−2−3)2(0)2−(−4)2=(−3)2−(−5)20−16=9−25−16=−16         TRUE_

Conclusion:

The solution to the given equation (x+2)2−(x−2)2=(x−1)2−(x−3)2is x=−2

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Chapter 5.6, Problem 60WE
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Chapter 5.6, Problem 62WE

Chapter 5 Solutions

Algebra: Structure And Method, Book 1

Ch. 5.1 - Prob. 1OECh. 5.1 - Prob. 2OECh. 5.1 - Prob. 3OECh. 5.1 - Prob. 4OECh. 5.1 - Prob. 5OECh. 5.1 - Prob. 6OECh. 5.1 - Prob. 7OECh. 5.1 - Prob. 8OECh. 5.1 - Prob. 9OECh. 5.1 - Prob. 10OE
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Prob. 45WECh. 5.6 - Prob. 46WECh. 5.6 - Prob. 47WECh. 5.6 - Prob. 48WECh. 5.6 - Prob. 49WECh. 5.6 - Prob. 50WECh. 5.6 - Prob. 51WECh. 5.6 - Prob. 52WECh. 5.6 - Prob. 53WECh. 5.6 - Prob. 54WECh. 5.6 - Prob. 55WECh. 5.6 - Prob. 56WECh. 5.6 - Prob. 57WECh. 5.6 - Prob. 58WECh. 5.6 - Prob. 59WECh. 5.6 - Prob. 60WECh. 5.6 - Prob. 61WECh. 5.6 - Prob. 62WECh. 5.6 - Prob. 63WECh. 5.6 - Prob. 64WECh. 5.6 - Prob. 65WECh. 5.6 - Prob. 66WECh. 5.6 - Prob. 1MRECh. 5.6 - Prob. 2MRECh. 5.6 - Prob. 3MRECh. 5.6 - Prob. 4MRECh. 5.6 - Prob. 5MRECh. 5.6 - Prob. 6MRECh. 5.6 - Prob. 7MRECh. 5.6 - Prob. 8MRECh. 5.6 - Prob. 9MRECh. 5.6 - Prob. 10MRECh. 5.6 - Prob. 11MRECh. 5.6 - Prob. 12MRECh. 5.6 - Prob. 1STCh. 5.6 - Prob. 2STCh. 5.6 - Prob. 3STCh. 5.6 - Prob. 4STCh. 5.6 - Prob. 5STCh. 5.6 - Prob. 6STCh. 5.6 - Prob. 7STCh. 5.6 - Prob. 8STCh. 5.6 - Prob. 9STCh. 5.6 - Prob. 10STCh. 5.6 - Prob. 11STCh. 5.6 - Prob. 12STCh. 5.7 - Prob. 1OECh. 5.7 - Prob. 2OECh. 5.7 - Prob. 3OECh. 5.7 - Prob. 4OECh. 5.7 - Prob. 5OECh. 5.7 - Prob. 6OECh. 5.7 - Prob. 7OECh. 5.7 - Prob. 8OECh. 5.7 - Prob. 9OECh. 5.7 - Prob. 10OECh. 5.7 - Prob. 11OECh. 5.7 - Prob. 12OECh. 5.7 - Prob. 13OECh. 5.7 - Prob. 14OECh. 5.7 - Prob. 15OECh. 5.7 - Prob. 16OECh. 5.7 - Prob. 17OECh. 5.7 - Prob. 18OECh. 5.7 - Prob. 19OECh. 5.7 - Prob. 20OECh. 5.7 - Prob. 21OECh. 5.7 - Prob. 22OECh. 5.7 - Prob. 23OECh. 5.7 - Prob. 24OECh. 5.7 - Prob. 25OECh. 5.7 - Prob. 1WECh. 5.7 - Prob. 2WECh. 5.7 - Prob. 3WECh. 5.7 - Prob. 4WECh. 5.7 - Prob. 5WECh. 5.7 - Prob. 6WECh. 5.7 - Prob. 7WECh. 5.7 - Prob. 8WECh. 5.7 - Prob. 9WECh. 5.7 - Prob. 10WECh. 5.7 - Prob. 11WECh. 5.7 - Prob. 12WECh. 5.7 - Prob. 13WECh. 5.7 - Prob. 14WECh. 5.7 - Prob. 15WECh. 5.7 - Prob. 16WECh. 5.7 - Prob. 17WECh. 5.7 - Prob. 18WECh. 5.7 - Prob. 19WECh. 5.7 - Prob. 20WECh. 5.7 - Prob. 21WECh. 5.7 - Prob. 22WECh. 5.7 - Prob. 23WECh. 5.7 - Prob. 24WECh. 5.7 - Prob. 25WECh. 5.7 - Prob. 26WECh. 5.7 - Prob. 27WECh. 5.7 - Prob. 28WECh. 5.7 - Prob. 29WECh. 5.7 - Prob. 30WECh. 5.7 - Prob. 31WECh. 5.7 - Prob. 32WECh. 5.7 - Prob. 33WECh. 5.7 - Prob. 34WECh. 5.7 - Prob. 35WECh. 5.7 - Prob. 36WECh. 5.7 - Prob. 37WECh. 5.7 - Prob. 38WECh. 5.7 - Prob. 39WECh. 5.7 - Prob. 40WECh. 5.7 - Prob. 41WECh. 5.7 - Prob. 42WECh. 5.7 - Prob. 43WECh. 5.7 - Prob. 44WECh. 5.7 - Prob. 45WECh. 5.7 - Prob. 46WECh. 5.7 - Prob. 47WECh. 5.7 - Prob. 48WECh. 5.7 - Prob. 49WECh. 5.7 - Prob. 50WECh. 5.7 - Prob. 51WECh. 5.7 - Prob. 52WECh. 5.7 - Prob. 53WECh. 5.7 - Prob. 54WECh. 5.7 - Prob. 55WECh. 5.7 - Prob. 56WECh. 5.7 - Prob. 1MRECh. 5.7 - Prob. 2MRECh. 5.7 - Prob. 3MRECh. 5.7 - Prob. 4MRECh. 5.7 - Prob. 5MRECh. 5.7 - Prob. 6MRECh. 5.7 - Prob. 7MRECh. 5.7 - Prob. 8MRECh. 5.7 - Prob. 9MRECh. 5.7 - Prob. 10MRECh. 5.7 - Prob. 11MRECh. 5.7 - Prob. 12MRECh. 5.8 - Prob. 1OECh. 5.8 - Prob. 2OECh. 5.8 - Prob. 3OECh. 5.8 - Prob. 4OECh. 5.8 - Prob. 5OECh. 5.8 - Prob. 6OECh. 5.8 - Prob. 7OECh. 5.8 - Prob. 8OECh. 5.8 - Prob. 9OECh. 5.8 - Prob. 10OECh. 5.8 - Prob. 11OECh. 5.8 - Prob. 12OECh. 5.8 - Prob. 13OECh. 5.8 - Prob. 14OECh. 5.8 - Prob. 15OECh. 5.8 - Prob. 16OECh. 5.8 - Prob. 17OECh. 5.8 - Prob. 18OECh. 5.8 - Prob. 19OECh. 5.8 - Prob. 1WECh. 5.8 - Prob. 2WECh. 5.8 - Prob. 3WECh. 5.8 - Prob. 4WECh. 5.8 - Prob. 5WECh. 5.8 - Prob. 6WECh. 5.8 - Prob. 7WECh. 5.8 - Prob. 8WECh. 5.8 - Prob. 9WECh. 5.8 - Prob. 10WECh. 5.8 - Prob. 11WECh. 5.8 - Prob. 12WECh. 5.8 - Prob. 13WECh. 5.8 - Prob. 14WECh. 5.8 - Prob. 15WECh. 5.8 - Prob. 16WECh. 5.8 - Prob. 17WECh. 5.8 - Prob. 18WECh. 5.8 - Prob. 19WECh. 5.8 - Prob. 20WECh. 5.8 - Prob. 21WECh. 5.8 - Prob. 22WECh. 5.8 - Prob. 23WECh. 5.8 - Prob. 24WECh. 5.8 - Prob. 25WECh. 5.8 - Prob. 26WECh. 5.8 - Prob. 27WECh. 5.8 - Prob. 28WECh. 5.8 - Prob. 29WECh. 5.8 - Prob. 30WECh. 5.8 - Prob. 31WECh. 5.8 - Prob. 32WECh. 5.8 - Prob. 33WECh. 5.8 - Prob. 34WECh. 5.8 - Prob. 35WECh. 5.8 - Prob. 36WECh. 5.8 - Prob. 37WECh. 5.8 - Prob. 38WECh. 5.8 - Prob. 39WECh. 5.8 - Prob. 40WECh. 5.8 - Prob. 41WECh. 5.8 - Prob. 42WECh. 5.8 - Prob. 43WECh. 5.8 - Prob. 44WECh. 5.8 - Prob. 45WECh. 5.8 - Prob. 46WECh. 5.8 - Prob. 47WECh. 5.8 - Prob. 48WECh. 5.8 - Prob. 49WECh. 5.8 - Prob. 50WECh. 5.8 - Prob. 51WECh. 5.8 - Prob. 52WECh. 5.8 - Prob. 53WECh. 5.8 - Prob. 54WECh. 5.8 - Prob. 55WECh. 5.8 - Prob. 56WECh. 5.8 - Prob. 1MRECh. 5.8 - Prob. 2MRECh. 5.8 - Prob. 3MRECh. 5.8 - Prob. 4MRECh. 5.8 - Prob. 5MRECh. 5.8 - Prob. 6MRECh. 5.8 - Prob. 7MRECh. 5.8 - Prob. 8MRECh. 5.8 - Prob. 9MRECh. 5.8 - Prob. 10MRECh. 5.8 - Prob. 11MRECh. 5.8 - Prob. 12MRECh. 5.8 - Prob. 13MRECh. 5.8 - Prob. 14MRECh. 5.8 - Prob. 15MRECh. 5.8 - Prob. 16MRECh. 5.8 - Prob. 17MRECh. 5.8 - Prob. 18MRECh. 5.8 - Prob. 19MRECh. 5.8 - Prob. 20MRECh. 5.8 - Prob. 21MRECh. 5.8 - Prob. 22MRECh. 5.8 - Prob. 23MRECh. 5.8 - Prob. 24MRECh. 5.8 - Prob. 25MRECh. 5.8 - Prob. 26MRECh. 5.8 - Prob. 27MRECh. 5.8 - Prob. 28MRECh. 5.8 - Prob. 29MRECh. 5.8 - Prob. 30MRECh. 5.9 - Prob. 1OECh. 5.9 - Prob. 2OECh. 5.9 - Prob. 3OECh. 5.9 - Prob. 4OECh. 5.9 - Prob. 5OECh. 5.9 - Prob. 6OECh. 5.9 - Prob. 7OECh. 5.9 - Prob. 8OECh. 5.9 - Prob. 9OECh. 5.9 - Prob. 10OECh. 5.9 - Prob. 11OECh. 5.9 - Prob. 12OECh. 5.9 - Prob. 13OECh. 5.9 - Prob. 14OECh. 5.9 - Prob. 1WECh. 5.9 - Prob. 2WECh. 5.9 - Prob. 3WECh. 5.9 - Prob. 4WECh. 5.9 - Prob. 5WECh. 5.9 - Prob. 6WECh. 5.9 - Prob. 7WECh. 5.9 - Prob. 8WECh. 5.9 - Prob. 9WECh. 5.9 - Prob. 10WECh. 5.9 - Prob. 11WECh. 5.9 - Prob. 12WECh. 5.9 - Prob. 13WECh. 5.9 - Prob. 14WECh. 5.9 - Prob. 15WECh. 5.9 - Prob. 16WECh. 5.9 - Prob. 17WECh. 5.9 - Prob. 18WECh. 5.9 - Prob. 19WECh. 5.9 - Prob. 20WECh. 5.9 - Prob. 21WECh. 5.9 - Prob. 22WECh. 5.9 - Prob. 23WECh. 5.9 - Prob. 24WECh. 5.9 - Prob. 25WECh. 5.9 - Prob. 26WECh. 5.9 - Prob. 27WECh. 5.9 - Prob. 28WECh. 5.9 - Prob. 29WECh. 5.9 - Prob. 30WECh. 5.9 - Prob. 31WECh. 5.9 - Prob. 32WECh. 5.9 - Prob. 33WECh. 5.9 - Prob. 34WECh. 5.9 - Prob. 35WECh. 5.9 - Prob. 36WECh. 5.9 - Prob. 37WECh. 5.9 - Prob. 38WECh. 5.9 - Prob. 39WECh. 5.9 - Prob. 40WECh. 5.9 - Prob. 41WECh. 5.9 - Prob. 42WECh. 5.9 - Prob. 43WECh. 5.9 - Prob. 44WECh. 5.9 - Prob. 45WECh. 5.9 - Prob. 46WECh. 5.9 - Prob. 1MRECh. 5.9 - Prob. 2MRECh. 5.9 - Prob. 3MRECh. 5.9 - Prob. 4MRECh. 5.9 - Prob. 5MRECh. 5.9 - Prob. 6MRECh. 5.9 - Prob. 7MRECh. 5.9 - Prob. 8MRECh. 5.9 - Prob. 9MRECh. 5.9 - Prob. 10MRECh. 5.9 - Prob. 11MRECh. 5.9 - Prob. 12MRECh. 5.9 - Prob. 1STCh. 5.9 - Prob. 2STCh. 5.9 - Prob. 3STCh. 5.9 - Prob. 4STCh. 5.9 - Prob. 5STCh. 5.9 - Prob. 6STCh. 5.10 - Prob. 1OECh. 5.10 - Prob. 2OECh. 5.10 - Prob. 3OECh. 5.10 - Prob. 4OECh. 5.10 - Prob. 5OECh. 5.10 - Prob. 6OECh. 5.10 - Prob. 7OECh. 5.10 - Prob. 8OECh. 5.10 - Prob. 9OECh. 5.10 - Prob. 1WECh. 5.10 - Prob. 2WECh. 5.10 - Prob. 3WECh. 5.10 - Prob. 4WECh. 5.10 - Prob. 5WECh. 5.10 - Prob. 6WECh. 5.10 - Prob. 7WECh. 5.10 - Prob. 8WECh. 5.10 - Prob. 9WECh. 5.10 - Prob. 10WECh. 5.10 - Prob. 11WECh. 5.10 - Prob. 12WECh. 5.10 - Prob. 13WECh. 5.10 - Prob. 14WECh. 5.10 - Prob. 15WECh. 5.10 - Prob. 16WECh. 5.10 - Prob. 17WECh. 5.10 - Prob. 18WECh. 5.10 - Prob. 19WECh. 5.10 - Prob. 20WECh. 5.10 - Prob. 21WECh. 5.10 - Prob. 22WECh. 5.10 - Prob. 23WECh. 5.10 - Prob. 24WECh. 5.10 - Prob. 25WECh. 5.10 - Prob. 26WECh. 5.10 - Prob. 27WECh. 5.10 - Prob. 28WECh. 5.10 - Prob. 29WECh. 5.10 - Prob. 30WECh. 5.10 - Prob. 31WECh. 5.10 - Prob. 32WECh. 5.10 - Prob. 33WECh. 5.10 - Prob. 34WECh. 5.10 - Prob. 35WECh. 5.10 - Prob. 36WECh. 5.10 - Prob. 37WECh. 5.10 - Prob. 38WECh. 5.10 - Prob. 39WECh. 5.10 - Prob. 40WECh. 5.10 - Prob. 41WECh. 5.10 - Prob. 42WECh. 5.10 - Prob. 43WECh. 5.10 - Prob. 44WECh. 5.10 - Prob. 45WECh. 5.10 - Prob. 46WECh. 5.10 - Prob. 47WECh. 5.10 - Prob. 48WECh. 5.10 - Prob. 49WECh. 5.10 - Prob. 50WECh. 5.10 - Prob. 51WECh. 5.10 - Prob. 52WECh. 5.10 - Prob. 53WECh. 5.10 - Prob. 54WECh. 5.10 - Prob. 55WECh. 5.10 - Prob. 56WECh. 5.10 - Prob. 57WECh. 5.10 - Prob. 58WECh. 5.10 - Prob. 59WECh. 5.10 - Prob. 60WECh. 5.10 - Prob. 61WECh. 5.10 - Prob. 62WECh. 5.10 - Prob. 63WECh. 5.10 - Prob. 1MRECh. 5.10 - Prob. 2MRECh. 5.10 - Prob. 3MRECh. 5.10 - Prob. 4MRECh. 5.10 - Prob. 5MRECh. 5.10 - Prob. 6MRECh. 5.10 - Prob. 7MRECh. 5.10 - Prob. 8MRECh. 5.10 - Prob. 9MRECh. 5.10 - Prob. 10MRECh. 5.10 - Prob. 11MRECh. 5.10 - Prob. 12MRECh. 5.11 - Prob. 1OECh. 5.11 - Prob. 2OECh. 5.11 - Prob. 3OECh. 5.11 - Prob. 4OECh. 5.11 - Prob. 5OECh. 5.11 - Prob. 6OECh. 5.11 - Prob. 7OECh. 5.11 - Prob. 8OECh. 5.11 - Prob. 9OECh. 5.11 - Prob. 10OECh. 5.11 - Prob. 11OECh. 5.11 - Prob. 12OECh. 5.11 - Prob. 1WECh. 5.11 - Prob. 2WECh. 5.11 - Prob. 3WECh. 5.11 - Prob. 4WECh. 5.11 - Prob. 5WECh. 5.11 - Prob. 6WECh. 5.11 - Prob. 7WECh. 5.11 - Prob. 8WECh. 5.11 - Prob. 9WECh. 5.11 - Prob. 10WECh. 5.11 - Prob. 11WECh. 5.11 - Prob. 12WECh. 5.11 - Prob. 13WECh. 5.11 - Prob. 14WECh. 5.11 - Prob. 15WECh. 5.11 - Prob. 16WECh. 5.11 - Prob. 17WECh. 5.11 - Prob. 18WECh. 5.11 - Prob. 19WECh. 5.11 - Prob. 20WECh. 5.11 - Prob. 21WECh. 5.11 - Prob. 22WECh. 5.11 - Prob. 23WECh. 5.11 - Prob. 24WECh. 5.11 - Prob. 25WECh. 5.11 - Prob. 26WECh. 5.11 - Prob. 27WECh. 5.11 - Prob. 28WECh. 5.11 - Prob. 29WECh. 5.11 - Prob. 30WECh. 5.11 - Prob. 31WECh. 5.11 - Prob. 32WECh. 5.11 - Prob. 33WECh. 5.11 - Prob. 34WECh. 5.11 - Prob. 35WECh. 5.11 - Prob. 36WECh. 5.11 - Prob. 37WECh. 5.11 - Prob. 38WECh. 5.11 - Prob. 39WECh. 5.11 - Prob. 40WECh. 5.11 - Prob. 41WECh. 5.11 - Prob. 42WECh. 5.11 - Prob. 43WECh. 5.11 - Prob. 44WECh. 5.11 - Prob. 45WECh. 5.11 - Prob. 46WECh. 5.11 - Prob. 47WECh. 5.11 - Prob. 48WECh. 5.11 - Prob. 49WECh. 5.11 - Prob. 50WECh. 5.11 - Prob. 51WECh. 5.11 - Prob. 52WECh. 5.11 - Prob. 53WECh. 5.11 - Prob. 54WECh. 5.11 - Prob. 55WECh. 5.11 - Prob. 56WECh. 5.11 - Prob. 57WECh. 5.11 - Prob. 58WECh. 5.11 - Prob. 1MRECh. 5.11 - Prob. 2MRECh. 5.11 - Prob. 3MRECh. 5.11 - Prob. 4MRECh. 5.11 - Prob. 5MRECh. 5.11 - Prob. 6MRECh. 5.11 - Prob. 7MRECh. 5.11 - Prob. 8MRECh. 5.11 - Prob. 9MRECh. 5.11 - Prob. 10MRECh. 5.11 - Prob. 11MRECh. 5.11 - Prob. 12MRECh. 5.12 - Prob. 1OECh. 5.12 - Prob. 2OECh. 5.12 - Prob. 3OECh. 5.12 - Prob. 4OECh. 5.12 - Prob. 5OECh. 5.12 - Prob. 6OECh. 5.12 - Prob. 7OECh. 5.12 - Prob. 8OECh. 5.12 - Prob. 9OECh. 5.12 - Prob. 10OECh. 5.12 - Prob. 11OECh. 5.12 - Prob. 12OECh. 5.12 - Prob. 1WECh. 5.12 - Prob. 2WECh. 5.12 - Prob. 3WECh. 5.12 - Prob. 4WECh. 5.12 - Prob. 5WECh. 5.12 - Prob. 6WECh. 5.12 - Prob. 7WECh. 5.12 - Prob. 8WECh. 5.12 - Prob. 9WECh. 5.12 - Prob. 10WECh. 5.12 - Prob. 11WECh. 5.12 - Prob. 12WECh. 5.12 - Prob. 13WECh. 5.12 - Prob. 14WECh. 5.12 - Prob. 15WECh. 5.12 - Prob. 16WECh. 5.12 - Prob. 17WECh. 5.12 - Prob. 18WECh. 5.12 - Prob. 19WECh. 5.12 - Prob. 20WECh. 5.12 - Prob. 21WECh. 5.12 - Prob. 22WECh. 5.12 - Prob. 23WECh. 5.12 - Prob. 24WECh. 5.12 - Prob. 25WECh. 5.12 - Prob. 26WECh. 5.12 - Prob. 27WECh. 5.12 - Prob. 28WECh. 5.12 - Prob. 29WECh. 5.12 - Prob. 30WECh. 5.12 - Prob. 31WECh. 5.12 - Prob. 32WECh. 5.12 - Prob. 33WECh. 5.12 - Prob. 34WECh. 5.12 - Prob. 35WECh. 5.12 - Prob. 36WECh. 5.12 - Prob. 37WECh. 5.12 - Prob. 38WECh. 5.12 - Prob. 39WECh. 5.12 - Prob. 40WECh. 5.12 - Prob. 41WECh. 5.12 - Prob. 42WECh. 5.12 - Prob. 43WECh. 5.12 - Prob. 44WECh. 5.12 - Prob. 45WECh. 5.12 - Prob. 46WECh. 5.12 - Prob. 47WECh. 5.12 - Prob. 48WECh. 5.12 - Prob. 49WECh. 5.12 - Prob. 50WECh. 5.12 - Prob. 51WECh. 5.12 - Prob. 52WECh. 5.12 - Prob. 53WECh. 5.12 - Prob. 54WECh. 5.12 - Prob. 55WECh. 5.12 - Prob. 1MRECh. 5.12 - Prob. 2MRECh. 5.12 - Prob. 3MRECh. 5.12 - Prob. 4MRECh. 5.12 - Prob. 5MRECh. 5.12 - Prob. 6MRECh. 5.12 - Prob. 7MRECh. 5.12 - Prob. 8MRECh. 5.12 - Prob. 9MRECh. 5.12 - Prob. 10MRECh. 5.12 - Prob. 11MRECh. 5.12 - Prob. 12MRECh. 5.13 - Prob. 1PCh. 5.13 - Prob. 2PCh. 5.13 - Prob. 3PCh. 5.13 - Prob. 4PCh. 5.13 - Prob. 5PCh. 5.13 - Prob. 6PCh. 5.13 - Prob. 7PCh. 5.13 - Prob. 8PCh. 5.13 - Prob. 9PCh. 5.13 - Prob. 10PCh. 5.13 - Prob. 11PCh. 5.13 - Prob. 12PCh. 5.13 - Prob. 13PCh. 5.13 - Prob. 14PCh. 5.13 - Prob. 15PCh. 5.13 - Prob. 16PCh. 5.13 - Prob. 17PCh. 5.13 - Prob. 18PCh. 5.13 - Prob. 19PCh. 5.13 - Prob. 20PCh. 5.13 - Prob. 21PCh. 5.13 - Prob. 22PCh. 5.13 - Prob. 23PCh. 5.13 - Prob. 24PCh. 5.13 - Prob. 25PCh. 5.13 - Prob. 26PCh. 5.13 - Prob. 27PCh. 5.13 - Prob. 28PCh. 5.13 - Prob. 29PCh. 5.13 - Prob. 30PCh. 5.13 - Prob. 31PCh. 5.13 - Prob. 32PCh. 5.13 - Prob. 1MRECh. 5.13 - Prob. 2MRECh. 5.13 - Prob. 3MRECh. 5.13 - Prob. 4MRECh. 5.13 - Prob. 5MRECh. 5.13 - Prob. 6MRECh. 5.13 - Prob. 7MRECh. 5.13 - Prob. 8MRECh. 5.13 - Prob. 9MRECh. 5.13 - Prob. 10MRECh. 5.13 - Prob. 11MRECh. 5.13 - Prob. 12MRECh. 5.13 - Prob. 13MRECh. 5.13 - Prob. 14MRECh. 5.13 - Prob. 15MRECh. 5.13 - Prob. 1STCh. 5.13 - Prob. 2STCh. 5.13 - Prob. 3STCh. 5.13 - Prob. 4STCh. 5.13 - Prob. 5STCh. 5.13 - Prob. 6STCh. 5.13 - Prob. 7STCh. 5.13 - Prob. 8STCh. 5.13 - Prob. 9STCh. 5.13 - Prob. 1ECh. 5.13 - Prob. 2ECh. 5.13 - Prob. 3ECh. 5.13 - Prob. 4ECh. 5.13 - Prob. 5ECh. 5.13 - Prob. 6ECh. 5.13 - Prob. 7ECh. 5 - Prob. 1CRCh. 5 - Prob. 2CRCh. 5 - Prob. 3CRCh. 5 - Prob. 4CRCh. 5 - Prob. 5CRCh. 5 - Prob. 6CRCh. 5 - Prob. 7CRCh. 5 - Prob. 8CRCh. 5 - Prob. 9CRCh. 5 - Prob. 10CRCh. 5 - Prob. 11CRCh. 5 - Prob. 12CRCh. 5 - Prob. 13CRCh. 5 - Prob. 14CRCh. 5 - Prob. 15CRCh. 5 - Prob. 16CRCh. 5 - Prob. 17CRCh. 5 - Prob. 18CRCh. 5 - Prob. 19CRCh. 5 - Prob. 20CRCh. 5 - Prob. 21CRCh. 5 - Prob. 22CRCh. 5 - Prob. 23CRCh. 5 - Prob. 24CRCh. 5 - Prob. 1CTCh. 5 - Prob. 2CTCh. 5 - Prob. 3CTCh. 5 - Prob. 4CTCh. 5 - Prob. 5CTCh. 5 - Prob. 6CTCh. 5 - Prob. 7CTCh. 5 - Prob. 8CTCh. 5 - Prob. 9CTCh. 5 - Prob. 10CTCh. 5 - Prob. 11CTCh. 5 - Prob. 12CTCh. 5 - Prob. 13CTCh. 5 - Prob. 14CTCh. 5 - Prob. 15CTCh. 5 - Prob. 16CTCh. 5 - Prob. 17CTCh. 5 - Prob. 18CTCh. 5 - Prob. 19CTCh. 5 - Prob. 20CTCh. 5 - Prob. 21CTCh. 5 - Prob. 22CTCh. 5 - Prob. 23CTCh. 5 - Prob. 24CTCh. 5 - Prob. 25CTCh. 5 - Prob. 26CTCh. 5 - Prob. 27CTCh. 5 - Prob. 28CTCh. 5 - Prob. 29CTCh. 5 - Prob. 30CTCh. 5 - Prob. 31CTCh. 5 - Prob. 32CTCh. 5 - Prob. 33CTCh. 5 - Prob. 34CTCh. 5 - Prob. 35CTCh. 5 - Prob. 36CTCh. 5 - Prob. 37CTCh. 5 - Prob. 38CTCh. 5 - Prob. 1CLRCh. 5 - Prob. 2CLRCh. 5 - Prob. 3CLRCh. 5 - Prob. 4CLRCh. 5 - Prob. 5CLRCh. 5 - Prob. 6CLRCh. 5 - Prob. 7CLRCh. 5 - Prob. 8CLRCh. 5 - Prob. 9CLRCh. 5 - Prob. 10CLRCh. 5 - Prob. 11CLRCh. 5 - Prob. 12CLRCh. 5 - Prob. 13CLRCh. 5 - Prob. 14CLRCh. 5 - Prob. 15CLRCh. 5 - Prob. 16CLRCh. 5 - Prob. 17CLRCh. 5 - Prob. 18CLRCh. 5 - Prob. 19CLRCh. 5 - Prob. 20CLRCh. 5 - Prob. 21CLRCh. 5 - Prob. 22CLRCh. 5 - Prob. 23CLRCh. 5 - Prob. 24CLRCh. 5 - Prob. 25CLRCh. 5 - Prob. 26CLRCh. 5 - Prob. 27CLRCh. 5 - Prob. 28CLRCh. 5 - Prob. 29CLRCh. 5 - Prob. 30CLRCh. 5 - Prob. 31CLRCh. 5 - Prob. 32CLRCh. 5 - Prob. 33CLRCh. 5 - Prob. 34CLRCh. 5 - Prob. 35CLRCh. 5 - Prob. 36CLRCh. 5 - Prob. 37CLRCh. 5 - Prob. 38CLRCh. 5 - Prob. 39CLRCh. 5 - Prob. 40CLRCh. 5 - Prob. 41CLRCh. 5 - Prob. 1MSCh. 5 - Prob. 2MSCh. 5 - Prob. 3MSCh. 5 - Prob. 4MSCh. 5 - Prob. 5MSCh. 5 - Prob. 1MPSCh. 5 - Prob. 2MPSCh. 5 - Prob. 3MPSCh. 5 - Prob. 4MPSCh. 5 - Prob. 5MPSCh. 5 - Prob. 6MPSCh. 5 - Prob. 7MPSCh. 5 - Prob. 8MPSCh. 5 - Prob. 9MPSCh. 5 - Prob. 10MPSCh. 5 - Prob. 11MPSCh. 5 - Prob. 12MPSCh. 5 - Prob. 13MPSCh. 5 - Prob. 14MPS

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