Explanation Given Information: The provided equation is 2 [ 4 − 2 ( 3 − x ) ] − 1 = 4 [ 2 ( 4 x − 3 ) + 7 ] − 25 . Formula used: Addition property: If a = b , then a + c = b + c , where a , b , and c are any real numbers. Division property: If a = b , then a c = b c , where a , b , and c are any real numbers and c ≠ 0 . Distributive property: For any real numbers a , b , c such that a ( b + c ) = a b + a c . The following steps are used to solve the equation: Step 1: Multiply the equations on both sided to remove the fractions or decimals. Step 2: Remove the parenthesis with the help of distributive property. Step 3: Collect the like terms from each side if it is necessary. Step 4: Separate the all variable terms on each side and all constants on each side with the help of addition property. Step 5: Collect the like terms from each side again if it is necessary. Step 6: Now solve the variable with the help of multiplication or division property. Step 7: Now check the solution in the provided equation. Calculation: Consider the provided equation. 2 [ 4 − 2 ( 3 − x ) ] − 1 = 4 [ 2 ( 4 x − 3 ) + 7 ] − 25 Apply distributive property to remove the parentheses on both sides of the equation. 8 − 4 ( 3 − x ) − 1 = 8 ( 4 x − 3 ) + 28 − 25 7 − 4 ( 3 − x ) = 8 ( 4 x − 3 ) + 3 Apply distributive property to remove the parentheses on both sides of the equation. 7 − 12 + 4 x = 32 x − 24 + 3 4 x − 5 = 32 x − 21 Apply addition property, add − 4 x to the both sides of the equation. 4 x − 5 − 4 x = 32 x − 21 − 4 x − 5 = 28 x − 21 Apply addition property, add 21 to both sides of the equation. − 5 + 21 = 28 x − 21 + 21 16 = 28 x By division property, divide both sides of the equation by 28 . 16 28 = 28 x 28 4 7 = x Check: Substitute x = 4 7 in the original equation

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ISBN: 9781323235911

Author: BITTINGER

Publisher: Pearson Custom Publishing

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Chapter 8.3, Problem 85ES

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To calculate: The solution of the equation 2[4−2(3−x)]−1=4[2(4x−3)+7]−25.

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Chapter 8.3, Problem 84ES

Chapter 8.3, Problem 86ES

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Ch. 8.1 - Objective 7.1a: Evaluate algebraic expressions by...Ch. 8.1 - Prob. 2SR Ch. 8.1 - Prob. 1DE Ch. 8.1 - Prob. 2DE Ch. 8.1 - Prob. 3DE Ch. 8.1 - Prob. 4DE Ch. 8.1 - Prob. 5DE Ch. 8.1 - Prob. 6DE Ch. 8.1 - Prob. 7DE Ch. 8.1 - Prob. 8DE

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The solution of the equation 2 [ 4 − 2 ( 3 − x ) ] − 1 = 4 [ 2 ( 4 x − 3 ) + 7 ] − 25 .

Solution Summary: The author calculates the solution of the equation 2(3-x-)right, which is 47.

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To calculate: The solution of the equation 2[4−2(3−x)]−1=4[2(4x−3)+7]−25.

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