Algebra: Structure And Method, Book 1
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
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Chapter 3.5, Problem 46WE
To determine

To solve the equation:

  2[5(w+3)−(w+1)]=3(1+w)

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

Expert Solution & Answer
Check Mark

Answer to Problem 46WE

Equation has only one solution: w=6.5 .

Explanation of Solution

Given:

  2[5(w+3)−(w+1)]=3(1+w)

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

Calculation:

In order to solve the equation:

  2[5(w+3)−(w+1)]=3(1+w)

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

  2[5(w+3)−(w+1)]=3(1+w)2[5w+15−w−1]=3+3w2[4w−14]=3+3w8w−28=3+3w

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

  8w−28=3+3w⇒8w−3w=3+28⇒5w=31

Now, isolate the variable by dividing both sides of above by 5, as

  5w=31⇒5w5=315⇒w=6.5

Thus, the given equation has one solution w=6.5 .

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Chapter 3 Solutions

Algebra: Structure And Method, Book 1

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