Textbook Question
In Exercises 121–128, write each English phrase as an algebraic expression. Then simplify the expression. Let x represent the number. A number decreased by the sum of the number and four
Ch. P - Fundamental Concepts of Algebra
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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Table of contents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
Chapter 1, Problem 126
In Exercises 121–128, write each English phrase as an algebraic expression. Then simplify the expression. Let x represent the number. The difference between the product of six and a number and negative two times the number
Verified step by step guidance1
Step 1: Identify the key components of the English phrase. The phrase mentions 'the product of six and a number,' 'negative two times the number,' and 'the difference between' these two quantities. Let x represent the number.
Step 2: Translate 'the product of six and a number' into an algebraic expression. This is written as .
Step 3: Translate 'negative two times the number' into an algebraic expression. This is written as .
Step 4: Combine these expressions to represent 'the difference between the product of six and a number and negative two times the number.' This is written as .
Step 5: Simplify the expression by resolving the subtraction of a negative term. This becomes . Combine like terms to simplify further.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Algebraic Expressions
An algebraic expression is a mathematical phrase that can include numbers, variables, and operation symbols. In this context, it represents a relationship or operation involving a variable, such as 'x'. Understanding how to translate English phrases into algebraic expressions is crucial for solving algebra problems.
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Introduction to Algebraic Expressions
Product and Difference
The product refers to the result of multiplying two or more numbers or expressions, while the difference is the result of subtracting one number from another. In the given question, recognizing how to express 'the product of six and a number' and 'the difference' between two expressions is essential for forming the correct algebraic expression.
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Simplification of Expressions
Simplification involves reducing an algebraic expression to its simplest form by combining like terms and performing operations. This process is important for making expressions easier to work with and understand. In this exercise, after forming the algebraic expression, simplifying it will help clarify the relationship between the variables involved.
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Related Practice
Textbook Question
In Exercises 121–128, write each English phrase as an algebraic expression. Then simplify the expression. Let x represent the number. Eight decreased by three times the sum of a number and six
Textbook Question
Simplify each complex rational expression. [3-1/(x+3)]/[3+1/(x+3)]
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Textbook Question
In Exercises 121–128, write each English phrase as an algebraic expression. Then simplify the expression. Let x represent the number. Six times the product of negative five and a number
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Textbook Question
Exercises 159–161 will help you prepare for the material covered in the next section. If 6.2 is multiplied by 10^3, what does this multiplication do to the decimal point in 6.2?
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