Answer Equation has only one solution m = − 3.5 . Explanation Given: 5 x + 2 ( 1 − x ) = 2 ( 2 x − 1 ) Concept Used: An equation that is true for all the values of variable has infinitely many solutions. And an equation that is not true for any value of the variable has no solution. Steps to solve a linear equation: Use distributive property to remove any grouping symbol. Simplify the expression in each side of the equation. Collect the variable terms on one side of the equation and the constant on the other side. Isolate the variable Calculation: In order to solve the equation: 5 ( 2 m + 3 ) − ( 1 − 2 m ) = 2 [ 3 ( 3 + 2 m ) − ( 3 − m ) ] First, use distributive property to remove grouping symbol from each sides, as 5 ( 2 m + 3 ) − ( 1 − 2 m ) = 2 [ 3 ( 3 + 2 m ) − ( 3 − m ) ] 10 m + 6 − 1 + 2 m = 2 [ 9 + 6 m − 3 + m ] 12 m + 5 = 2 [ 7 m + 6 ] 12 m + 5 = 14 m + 12 Now, collect the variable terms on one side of the equation and the constant on the other side, as 12 m + 5 = 14 m + 12 ⇒ 5 − 12 = 14 m − 12 m ⇒ − 7 = 2 m ⇒ 2 m = − 7 Now, isolate the variable by dividing both sides of above by 2, as 2 m = − 7 ⇒ 2 m 2 = − 7 2 ⇒ m = − 3.5 Thus, the given equation has one solution m = − 3.5 .

(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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Question

Chapter 3.5, Problem 47WE

To determine

To solve the equation:

5(2m+3)−(1−2m)=2[3(3+2m)−(3−m)]

Also determine whether the equation is an identity or has no solution.

Expert Solution & Answer

Answer to Problem 47WE

Equation has only one solution m=−3.5 .

Explanation of Solution

Given:

5x+2(1−x)=2(2x−1)

Concept Used:

An equation that is true for all the values of variable has infinitely many solutions. And an equation that is not true for any value of the variable has no solution.
Steps to solve a linear equation:

Use distributive property to remove any grouping symbol.
Simplify the expression in each side of the equation.
Collect the variable terms on one side of the equation and the constant on the other side.
Isolate the variable

Calculation:

In order to solve the equation:

5(2m+3)−(1−2m)=2[3(3+2m)−(3−m)]

First, use distributive property to remove grouping symbol from each sides, as

5(2m+3)−(1−2m)=2[3(3+2m)−(3−m)]10m+6−1+2m=2[9+6m−3+m]12m+5=2[7m+6]12m+5=14m+12

Now, collect the variable terms on one side of the equation and the constant on the other side, as

12m+5=14m+12⇒5−12=14m−12m⇒−7=2m⇒2m=−7

Now, isolate the variable by dividing both sides of above by 2, as

2m=−7⇒2m2=−72⇒m=−3.5

Thus, the given equation has one solution m=−3.5 .

Chapter 3.5, Problem 46WE

Chapter 3.5, Problem 48WE

Chapter 3 Solutions

Algebra: Structure And Method, Book 1

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To solve the equation: 5 ( 2 m + 3 ) − ( 1 − 2 m ) = 2 [ 3 ( 3 + 2 m ) − ( 3 − m ) ] Also determine whether the equation is an identity or has no solution.