Answer Equation has only one solution x = − 1 . Explanation Given: x − 2 3 = 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 has no solution. Steps to solve a linear equation: Use distributive property to eliminate any grouping symbol. Simplify the expression in each side of the equation. Collect the variables on one side of the equation and the constants on the other side. Isolate the variable. Calculation: In order to solve the equation: x − 2 3 = x First, isolate the variable first by multiplying both sides of above with 3, as x − 2 3 = x ⇒ x − 2 3 × 3 = x × 3 ⇒ x − 2 = 3 x Now, collect the variables on one side of the equation and the constants on the other side, as x − 2 = 3 x ⇒ − 2 = 3 x − x ⇒ − 2 = 2 x ⇒ 2 x = − 2 ⇒ 2 x 2 = − 2 2 ⇒ x = − 1 Thus, the given equation has one solution x = − 1 .

(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 26WE

To determine

To solve: the equation

x−23=x

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

Expert Solution & Answer

Answer to Problem 26WE

Equation has only one solution x=−1 .

Explanation of Solution

Given:

x−23=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 has no solution.
Steps to solve a linear equation:

Use distributive property to eliminate any grouping symbol.
Simplify the expression in each side of the equation.
Collect the variables on one side of the equation and the constants on the other side.
Isolate the variable.

Calculation:

In order to solve the equation:

x−23=x

First, isolate the variable first by multiplying both sides of above with 3, as

x−23=x⇒x−23×3=x×3⇒x−2=3x

Now, collect the variables on one side of the equation and the constants on the other side, as

x−2=3x⇒−2=3x−x⇒−2=2x⇒2x=−2⇒2x2=−22⇒x=−1

Thus, the given equation has one solution x=−1 .

Chapter 3.5, Problem 25WE

Chapter 3.5, Problem 27WE

Chapter 3 Solutions

Algebra: Structure And Method, Book 1

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