Explanation Given Information: The provided equation is 2 7 x − 1 2 x = 3 4 x + 1 . Formula used: Addition property: If a = b , then a + c = b + c , where a , b , and c are any real numbers. Multiplication property: If a = b , then a ⋅ c = b ⋅ c , where a , b , and c are any real numbers and c ≠ 0 . Division property: If a = b , then a c = b c , where a , b , and c are any real numbers and c ≠ 0 . There are following steps to solve an equation with fractions. Step 1: Obtain the least common denominator (LCD) of all the fractional terms on both sides of the given equation. Step 2: Multiply both sides of the equation by the LCD to convert the provided equation without fractions. Step 3: Remove the parentheses (if any) by applying the distributive property. For any real numbers a , b , c , such that a ( b + c ) = a b + a c . Calculation: Consider the provided equation. 2 7 x − 1 2 x = 3 4 x + 1 Find the LCD of the denominators. The LCD of 2, 4, and 7 is 28. Multiply both sides of the equation by 28. 28 ( 2 7 x − 1 2 x ) = 28 ( 3 4 x + 1 ) Now, apply the distributive property on both sides of the equation. 28 ( 2 7 x ) − 28 ( 1 2 x ) = 28 ( 3 4 x ) + 28 8 x − 14 x = 21 x + 28 − 6 x = 21 x + 28 Apply the addition property, add − 21 x to both sides of the equation by. − 6 x − 21 x = 21 x + 28 − 21 x − 27 x = 28 Apply the division property, divide both sides of the equation by − 27

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Author: BITTINGER

Publisher: Pearson Custom Publishing

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Chapter 8.3, Problem 57ES

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Chapter 8.3, Problem 56ES

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The solution of the equation 2 7 x − 1 2 x = 3 4 x + 1 and check it

Solution Summary: The author explains how to solve an equation with tions by obtaining the least common denominator of all the tional terms on both sides of the equation.

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