Textbook Question
In Exercises 1–6, find all numbers that must be excluded from the domain of each rational expression. (x+5)/(x2−25)
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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 3
In Exercises 1–16, evaluate each algebraic expression for the given value or values of the variable(s). 6x-y, for x=3 and y=8
Verified step by step guidance1
Substitute the given values of the variables into the algebraic expression. Replace x with 3 and y with 8 in the expression 6x - y.
The expression becomes 6(3) - 8. Simplify the multiplication first by calculating 6 times 3.
After performing the multiplication, simplify the expression further by subtracting 8 from the result of 6(3).
Verify your work by double-checking the substitution and calculations to ensure accuracy.
The simplified result represents the value of the expression for the given values of x and y.
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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. It represents a value that can change depending on the values assigned to its variables. For example, in the expression 6x - y, 'x' and 'y' are variables that can take on different numerical values.
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Substitution
Substitution is the process of replacing a variable in an expression with a specific value. This is a fundamental technique in algebra that allows us to evaluate expressions. In the given problem, substituting x with 3 and y with 8 transforms the expression 6x - y into 6(3) - 8.
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Order of Operations
The order of operations is a set of rules that dictates the sequence in which calculations are performed in an expression. The common acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) helps remember this order. Following these rules ensures that expressions are evaluated correctly, such as calculating multiplication before subtraction in the expression 6(3) - 8.
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Related Practice
Textbook Question
In Exercises 1–10, factor out the greatest common factor. 3x2+6x
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Textbook Question
Evaluate each expression in Exercises 1–12, or indicate that the root is not a real number. −√36
Textbook Question
In Exercises 1–4, is the algebraic expression a polynomial? If it is, write the polynomial in standard form. 2x+3x2−5
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Textbook Question
Is the algebraic expression a polynomial? If it is, write the polynomial in standard form. (2x+3)/x
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Textbook Question
Evaluate each exponential expression in Exercises 1–22. (−2)6
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