Explanation Given Information: The provided equation is 3 x 5 − 9 − 3 x 10 = 6 10 − 3 x + 6 10 . Formula used: Subtraction property: The resultant equation will be equivalent to the original equation, if the same quantity will subtracted to both sides of the equation. Division property: The resultant equation will be equivalent to the original equation, if the same non-zero quantity is divided on both sides of the equation. 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 , a ( b + c ) = a b + a c . Calculation: Consider the provided equation. 3 x 5 − 9 − 3 x 10 = 6 10 − 3 x + 6 10 3 x 5 − 9 − 3 x 10 = 6 10 − 3 x + 6 10 Find the LCD of the denominators. The LCD of 5 and 10 is 10. Multiply both sides of the equation by 10. 10 [ 3 x 5 − 9 − 3 x 10 ] = 10 [ 6 10 − 3 x + 6 10 ] Now, apply the distributive property on both sides of the equation. 10 ( 3 x 5 ) − 10 ( 9 − 3 x 10 ) = 10 ( 6 10 ) − 10 ( 3 x + 6 10 ) 2 ( 3 x ) − 1 ( 9 − 3 x ) = 1 ( 6 ) − ( 3 x + 6 ) 6 x − 9 + 3 x = 6 − 3 x − 6 9 x − 9 = − 3 x Apply the subtraction property stated above, subtract both sides of the equation by 9 x . 9 x − 9 − 9 x = − 3 x − 9 x − 12 x = − 9 Apply the division property stated above, divide both sides of the equation by − 12 . − 12 x − 12 = − 9 − 12 x = 3 4 Check: Substitute 3 4 for x in the original equation

Bundle: Elementary Technical Mathematics, Loose-leaf Version, 12th + WebAssign Printed Access Card, Single-Term

12th Edition

ISBN: 9781337890199

Author: Dale Ewen

Publisher: Cengage Learning

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Chapter 6.4, Problem 24E

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To calculate: The solution of the equation 3x5−9−3x10=610−3x+610 and check it.

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Chapter 6.4, Problem 23E

Chapter 6.4, Problem 25E

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Chapter 6 Solutions

Bundle: Elementary Technical Mathematics, Loose-leaf Version, 12th + WebAssign Printed Access Card, Single-Term

Ch. 6.1 - Solve each equation and check: x+2=8 Ch. 6.1 - Prob. 2E Ch. 6.1 - Prob. 3E Ch. 6.1 - Solve each equation and check: 23n=6 Ch. 6.1 - Solve each equation and check: w712=3 Ch. 6.1 - Prob. 6E Ch. 6.1 - Solve each equation and check: x13=1.5 Ch. 6.1 - Solve each equation and check: n+12=5 Ch. 6.1 - Solve each equation and check: 3b=15.6 Ch. 6.1 - Solve each equation and check: y17=25

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The solution of the equation 3 x 5 − 9 − 3 x 10 = 6 10 − 3 x + 6 10 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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To calculate: The solution of the equation 3x5−9−3x10=610−3x+610 and check it.

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Chapter 6 Solutions