Algebra: Structure And Method, Book 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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Concept explainers

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.

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Question

Chapter 3.5, Problem 28WE

To determine

To solve: the equation

6−4y2=y

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

Expert Solution & Answer

Answer to Problem 28WE

Equation has only one solution y=1 .

Explanation of Solution

Given:

6−4y2=y

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:

6−4y2=y

First, isolate the variable first by multiplying both sides of given equation with 2, as

6−4y2=y⇒6−4y2×2=y×2⇒6−4y=2y

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

6−4y=2y⇒6=2y+4y⇒6=6y⇒6y=6⇒6y6=66⇒y=1

Thus, the given equation has one solution y=1 .

Chapter 3.5, Problem 27WE

Chapter 3.5, Problem 29WE

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

Ch. 3.1 - Prob. 11OE Ch. 3.1 - Prob. 12OE Ch. 3.1 - Prob. 13OE Ch. 3.1 - Prob. 14OE Ch. 3.1 - Prob. 15OE Ch. 3.1 - Prob. 16OE Ch. 3.1 - Prob. 17OE Ch. 3.1 - Prob. 18OE Ch. 3.1 - Prob. 19OE Ch. 3.1 - Prob. 20OE Ch. 3.1 - Prob. 21OE Ch. 3.1 - Prob. 1WE Ch. 3.1 - Prob. 2WE Ch. 3.1 - Prob. 3WE Ch. 3.1 - Prob. 4WE Ch. 3.1 - Prob. 5WE Ch. 3.1 - Prob. 6WE Ch. 3.1 - Prob. 7WE Ch. 3.1 - Prob. 8WE Ch. 3.1 - Prob. 9WE Ch. 3.1 - Prob. 10WE Ch. 3.1 - Prob. 11WE Ch. 3.1 - Prob. 12WE Ch. 3.1 - Prob. 13WE Ch. 3.1 - Prob. 14WE Ch. 3.1 - Prob. 15WE Ch. 3.1 - Prob. 16WE Ch. 3.1 - Prob. 17WE Ch. 3.1 - Prob. 18WE Ch. 3.1 - Prob. 19WE Ch. 3.1 - Prob. 20WE Ch. 3.1 - Prob. 21WE Ch. 3.1 - Prob. 22WE Ch. 3.1 - Prob. 23WE Ch. 3.1 - Prob. 24WE Ch. 3.1 - Prob. 25WE Ch. 3.1 - Prob. 26WE Ch. 3.1 - Prob. 27WE Ch. 3.1 - Prob. 28WE Ch. 3.1 - Prob. 29WE Ch. 3.1 - Prob. 30WE Ch. 3.1 - Prob. 31WE Ch. 3.1 - Prob. 32WE Ch. 3.1 - Prob. 33WE Ch. 3.1 - Prob. 34WE Ch. 3.1 - Prob. 35WE Ch. 3.1 - Prob. 36WE Ch. 3.1 - Prob. 37WE Ch. 3.1 - Prob. 38WE Ch. 3.1 - Prob. 39WE Ch. 3.1 - Prob. 40WE Ch. 3.1 - Prob. 41WE Ch. 3.1 - Prob. 42WE Ch. 3.1 - Prob. 43WE Ch. 3.1 - Prob. 44WE Ch. 3.1 - Prob. 45WE Ch. 3.1 - Prob. 46WE Ch. 3.1 - Prob. 47WE Ch. 3.1 - Prob. 48WE Ch. 3.1 - Prob. 49WE Ch. 3.1 - Prob. 50WE Ch. 3.1 - Prob. 51WE Ch. 3.1 - Prob. 52WE Ch. 3.1 - Prob. 53WE Ch. 3.1 - Prob. 54WE Ch. 3.1 - Prob. 55WE Ch. 3.1 - Prob. 56WE Ch. 3.1 - Prob. 57WE Ch. 3.1 - Prob. 58WE Ch. 3.1 - Prob. 59WE Ch. 3.1 - Prob. 60WE Ch. 3.1 - Prob. 1P Ch. 3.1 - Prob. 2P Ch. 3.1 - Prob. 3P Ch. 3.1 - Prob. 4P Ch. 3.1 - Prob. 5P Ch. 3.1 - Prob. 6P Ch. 3.1 - Prob. 7P Ch. 3.1 - Prob. 8P Ch. 3.1 - Prob. 9P Ch. 3.1 - Prob. 10P Ch. 3.1 - Prob. 11P Ch. 3.1 - Prob. 12P Ch. 3.1 - Prob. 13P Ch. 3.1 - Prob. 14P Ch. 3.1 - Prob. 15P Ch. 3.1 - Prob. 16P Ch. 3.1 - Prob. 17P Ch. 3.1 - Prob. 18P Ch. 3.1 - Prob. 19P Ch. 3.1 - Prob. 20P Ch. 3.1 - Prob. 1MRE Ch. 3.1 - Prob. 2MRE Ch. 3.1 - Prob. 3MRE Ch. 3.1 - Prob. 4MRE Ch. 3.1 - Prob. 5MRE Ch. 3.1 - Prob. 6MRE Ch. 3.1 - 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Prob. 22WE Ch. 3.2 - Prob. 23WE Ch. 3.2 - Prob. 24WE Ch. 3.2 - Prob. 25WE Ch. 3.2 - Prob. 26WE Ch. 3.2 - Prob. 27WE Ch. 3.2 - Prob. 28WE Ch. 3.2 - Prob. 29WE Ch. 3.2 - Prob. 30WE Ch. 3.2 - Prob. 31WE Ch. 3.2 - Prob. 32WE Ch. 3.2 - Prob. 33WE Ch. 3.2 - Prob. 34WE Ch. 3.2 - Prob. 35WE Ch. 3.2 - Prob. 36WE Ch. 3.2 - Prob. 37WE Ch. 3.2 - Prob. 38WE Ch. 3.2 - Prob. 39WE Ch. 3.2 - Prob. 40WE Ch. 3.2 - Prob. 41WE Ch. 3.2 - Prob. 42WE Ch. 3.2 - Prob. 43WE Ch. 3.2 - Prob. 44WE Ch. 3.2 - Prob. 45WE Ch. 3.2 - Prob. 46WE Ch. 3.2 - Prob. 47WE Ch. 3.2 - Prob. 48WE Ch. 3.2 - Prob. 49WE Ch. 3.2 - Prob. 50WE Ch. 3.2 - Prob. 51WE Ch. 3.2 - Prob. 52WE Ch. 3.2 - Prob. 1P Ch. 3.2 - Prob. 2P Ch. 3.2 - Prob. 3P Ch. 3.2 - Prob. 4P Ch. 3.2 - Prob. 5P Ch. 3.2 - Prob. 6P Ch. 3.2 - Prob. 7P Ch. 3.2 - Prob. 8P Ch. 3.2 - Prob. 9P Ch. 3.2 - Prob. 10P Ch. 3.2 - Prob. 11P Ch. 3.2 - Prob. 12P Ch. 3.2 - Prob. 13P Ch. 3.2 - Prob. 14P Ch. 3.2 - Prob. 15P Ch. 3.2 - Prob. 16P Ch. 3.2 - Prob. 17P Ch. 3.2 - Prob. 18P Ch. 3.2 - Prob. 19P Ch. 3.2 - Prob. 20P Ch. 3.2 - Prob. 1MRE Ch. 3.2 - Prob. 2MRE Ch. 3.2 - Prob. 3MRE Ch. 3.2 - Prob. 4MRE Ch. 3.2 - Prob. 5MRE Ch. 3.2 - Prob. 6MRE Ch. 3.2 - Prob. 7MRE Ch. 3.2 - Prob. 8MRE Ch. 3.2 - Prob. 9MRE Ch. 3.2 - Prob. 10MRE Ch. 3.2 - Prob. 11MRE Ch. 3.2 - Prob. 12MRE Ch. 3.3 - Prob. 1OE Ch. 3.3 - Prob. 2OE Ch. 3.3 - Prob. 3OE Ch. 3.3 - Prob. 4OE Ch. 3.3 - Prob. 5OE Ch. 3.3 - Prob. 6OE Ch. 3.3 - Prob. 7OE Ch. 3.3 - Prob. 8OE Ch. 3.3 - Prob. 9OE Ch. 3.3 - Prob. 10OE Ch. 3.3 - Prob. 11OE Ch. 3.3 - Prob. 12OE Ch. 3.3 - Prob. 13OE Ch. 3.3 - Prob. 14OE Ch. 3.3 - Prob. 15OE Ch. 3.3 - Prob. 16OE Ch. 3.3 - Prob. 17OE Ch. 3.3 - Prob. 18OE Ch. 3.3 - Prob. 1WE Ch. 3.3 - Prob. 2WE Ch. 3.3 - Prob. 3WE Ch. 3.3 - Prob. 4WE Ch. 3.3 - Prob. 5WE Ch. 3.3 - Prob. 6WE Ch. 3.3 - Prob. 7WE Ch. 3.3 - Prob. 8WE Ch. 3.3 - Prob. 9WE Ch. 3.3 - Prob. 10WE Ch. 3.3 - Prob. 11WE Ch. 3.3 - Prob. 12WE Ch. 3.3 - Prob. 13WE Ch. 3.3 - Prob. 14WE Ch. 3.3 - Prob. 15WE Ch. 3.3 - Prob. 16WE Ch. 3.3 - Prob. 17WE Ch. 3.3 - 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Prob. 6MRE Ch. 3.3 - Prob. 7MRE Ch. 3.3 - Prob. 8MRE Ch. 3.3 - Prob. 9MRE Ch. 3.3 - Prob. 10MRE Ch. 3.3 - Prob. 11MRE Ch. 3.3 - Prob. 12MRE Ch. 3.3 - Prob. 1E Ch. 3.3 - Prob. 2E Ch. 3.3 - Prob. 3E Ch. 3.4 - Prob. 1P Ch. 3.4 - Prob. 2P Ch. 3.4 - Prob. 3P Ch. 3.4 - Prob. 4P Ch. 3.4 - Prob. 5P Ch. 3.4 - Prob. 6P Ch. 3.4 - Prob. 7P Ch. 3.4 - Prob. 8P Ch. 3.4 - Prob. 9P Ch. 3.4 - Prob. 10P Ch. 3.4 - Prob. 11P Ch. 3.4 - Prob. 12P Ch. 3.4 - Prob. 13P Ch. 3.4 - Prob. 14P Ch. 3.4 - Prob. 15P Ch. 3.4 - Prob. 16P Ch. 3.4 - Prob. 17P Ch. 3.4 - Prob. 18P Ch. 3.4 - Prob. 19P Ch. 3.4 - Prob. 20P Ch. 3.4 - Prob. 21P Ch. 3.4 - Prob. 22P Ch. 3.4 - Prob. 23P Ch. 3.4 - Prob. 24P Ch. 3.4 - Prob. 25P Ch. 3.4 - Prob. 26P Ch. 3.4 - Prob. 27P Ch. 3.4 - Prob. 28P Ch. 3.4 - Prob. 29P Ch. 3.4 - Prob. 30P Ch. 3.4 - Prob. 31P Ch. 3.4 - Prob. 32P Ch. 3.4 - Prob. 33P Ch. 3.4 - Prob. 1MRE Ch. 3.4 - Prob. 2MRE Ch. 3.4 - Prob. 3MRE Ch. 3.4 - Prob. 4MRE Ch. 3.4 - Prob. 5MRE Ch. 3.4 - Prob. 6MRE Ch. 3.4 - Prob. 7MRE Ch. 3.4 - Prob. 8MRE Ch. 3.4 - Prob. 9MRE Ch. 3.4 - Prob. 10MRE Ch. 3.4 - Prob. 11MRE Ch. 3.4 - Prob. 12MRE Ch. 3.5 - Prob. 1OE Ch. 3.5 - Prob. 2OE Ch. 3.5 - Prob. 3OE Ch. 3.5 - Prob. 4OE Ch. 3.5 - Prob. 5OE Ch. 3.5 - Prob. 6OE Ch. 3.5 - Prob. 7OE Ch. 3.5 - Prob. 8OE Ch. 3.5 - Prob. 9OE Ch. 3.5 - Prob. 10OE Ch. 3.5 - Prob. 11OE Ch. 3.5 - Prob. 12OE Ch. 3.5 - Prob. 1WE Ch. 3.5 - Prob. 2WE Ch. 3.5 - Prob. 3WE Ch. 3.5 - Prob. 4WE Ch. 3.5 - Prob. 5WE Ch. 3.5 - Prob. 6WE Ch. 3.5 - Prob. 7WE Ch. 3.5 - Prob. 8WE Ch. 3.5 - Prob. 9WE Ch. 3.5 - Prob. 10WE Ch. 3.5 - Prob. 11WE Ch. 3.5 - Prob. 12WE Ch. 3.5 - Prob. 13WE Ch. 3.5 - Prob. 14WE Ch. 3.5 - Prob. 15WE Ch. 3.5 - Prob. 16WE Ch. 3.5 - Prob. 17WE Ch. 3.5 - Prob. 18WE Ch. 3.5 - Prob. 19WE Ch. 3.5 - Prob. 20WE Ch. 3.5 - Prob. 21WE Ch. 3.5 - Prob. 22WE Ch. 3.5 - Prob. 23WE Ch. 3.5 - Prob. 24WE Ch. 3.5 - Prob. 25WE Ch. 3.5 - Prob. 26WE Ch. 3.5 - Prob. 27WE Ch. 3.5 - Prob. 28WE Ch. 3.5 - Prob. 29WE Ch. 3.5 - Prob. 30WE Ch. 3.5 - Prob. 31WE Ch. 3.5 - Prob. 32WE Ch. 3.5 - 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the equation 6 − 4 y 2 = y Also determine whether the equation is an identity or has no solution.

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To solve: the equation 6−4y2=y Also determine whether the equation is an identity or has no solution.

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To solve: the equation

6−4y2=y

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