Problem 108 Translate from English to an alg... [FREE SOLUTION]

91影视

Introductory Algebra for College Students

Robert Blitzer

$Math Studyset 91影视 Explanations$ Math

6 Edition

Chapter 1: Problem 108

Translate from English to an algebraic expression or equation, whichever is appropriate. Let the variable $x$ represent the number. A number decreased by $\frac{1}{3}$ is half of that number.

Short Answer

Expert verified

The algebraic equation that represents the given English statement is $x - \frac{1}{3} = \frac{x}{2}$.

Step by step solution

Identify the variable

In this problem, it is given to use $x$ to represent 'the number'. Therefore, 'a number' is represented as $x$.

Translate the expression 'a number decreased by $\frac{1}{3}$'

The term 'a number decreased by $\frac{1}{3}$' can be translated to $x-\frac{1}{3}$. In this expression, $x$ is 'the number' and $-\frac{1}{3}$ represents 'decreased by $\frac{1}{3}$'.

Translate the expression 'half of that number'

'Half of that number' can be translated as $\frac{1}{2}*x$ or simply $\frac{x}{2}$. In this expression, $x$ is 'the number' and '$\frac{1}{2}$' represents 'half'.

Formulate the equation

Since the problem states that 'a number decreased by $\frac{1}{3}$' is 'half of that number', these two expressions are set equal to each other. Therefore, the algebraic equation is $x - \frac{1}{3} = \frac{x}{2}$.

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91影视

Translate from English to an algebraic expression or equation, whichever is appropriate. Let the variable \(x\) represent the number. A number decreased by \(\frac{1}{3}\) is half of that number.

Short Answer

Step by step solution

Identify the variable

Translate the expression 'a number decreased by \(\frac{1}{3}\)'

Translate the expression 'half of that number'

Formulate the equation

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