Answer The given equation is an identity and has infinitely many solutions. Explanation Given: 1 3 ( 12 − 6 x ) = 4 − 2 x 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: 1 3 ( 12 − 6 x ) = 4 − 2 x First, collect the variable terms on one side of the equation and the constant on the other side. For that start by multiplying both sides of given equation with 3 and then simplify further, as 1 3 ( 12 − 6 x ) = 4 − 2 x ⇒ 1 3 ( 12 − 6 x ) × 3 = ( 4 − 2 x ) × 3 ⇒ 1 ( 12 − 6 x ) = 4 × 3 − 6 x ⇒ 12 − 6 x = 12 − 6 x ⇒ − 6 x + 6 x = 12 − 12 ⇒ 0 = 0 Now, the statement 0 = 0 is true for every value of variable x . Thus, the given equation is an identity. Thus, the given equation has infinitely many solutions.

(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 31WE

To determine

To solve the equation:

13(12−6x)=4−2x

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

Expert Solution & Answer

Answer to Problem 31WE

The given equation is an identity and has infinitely many solutions.

Explanation of Solution

Given:

13(12−6x)=4−2x

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:

13(12−6x)=4−2x

First, collect the variable terms on one side of the equation and the constant on the other side.

For that start by multiplying both sides of given equation with 3 and then simplify further, as

13(12−6x)=4−2x⇒13(12−6x)×3=(4−2x)×3⇒1(12−6x)=4×3−6x⇒12−6x=12−6x⇒−6x+6x=12−12⇒0=0

Now, the statement 0=0 is true for every value of variable x . Thus, the given equation is an identity.

Thus, the given equation has infinitely many solutions.

Chapter 3.5, Problem 30WE

Chapter 3.5, Problem 32WE

Chapter 3 Solutions

Algebra: Structure And Method, Book 1

Ch. 3.1 - Prob. 1OE Ch. 3.1 - Prob. 2OE Ch. 3.1 - Prob. 3OE Ch. 3.1 - Prob. 4OE Ch. 3.1 - Prob. 5OE Ch. 3.1 - Prob. 6OE Ch. 3.1 - Prob. 7OE Ch. 3.1 - Prob. 8OE Ch. 3.1 - Prob. 9OE Ch. 3.1 - Prob. 10OE

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To solve the equation: 1 3 ( 12 − 6 x ) = 4 − 2 x Also determine whether the equation is an identity or has no solution.