Textbook Question
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
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 121
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
Verified step by step guidance1
Start by translating the English phrase into an algebraic expression. The phrase 'a number' can be represented by the variable x.
The phrase 'the sum of the number and four' means we are adding the number (x) and 4 together. This can be written as (x + 4).
The phrase 'a number decreased by' indicates subtraction. So, we subtract the sum (x + 4) from the number (x). This gives the expression x - (x + 4).
Simplify the expression x - (x + 4) by distributing the negative sign across the parentheses. This results in x - x - 4.
Combine like terms in the simplified expression. The x terms cancel out, leaving -4 as the simplified result.
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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
Order of Operations
The order of operations is a set of rules that dictates the sequence in which mathematical operations should be performed to ensure consistent results. Commonly remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction), this concept is essential for simplifying expressions correctly after they are formed.
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Simplifying Expressions
Simplifying an expression involves combining like terms and performing operations to reduce it to its simplest form. This process often includes distributing, factoring, and reducing fractions. Mastery of simplification is vital for solving equations and understanding the relationships between variables.
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Related Practice
Textbook Question
Simplify each complex rational expression. (1/x-1/2)/(1/3-x/6)
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
In Exercises 111–120, use the order of operations to simplify each expression. 6(−4)−5(−3)/(9−10)
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Textbook Question
Add or subtract as indicated. 12/25x^2+11/15x^3