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State the name of the property illustrated: (6 • 3) • 9 = 6 • (3 • 9)
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Ch. P - Fundamental Concepts of Algebra
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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TOC.tableOfContents
- 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
Capitolo 1, Problema 13
In Exercises 1–16, evaluate each algebraic expression for the given value or values of the variable(s). 5(x+2)/(2x-14), for x=10
Guida verificata passo dopo passo1
Step 1: Start by substituting the given value of x (x = 10) into the algebraic expression 5(x + 2) / (2x - 14). This gives 5(10 + 2) / (2(10) - 14).
Step 2: Simplify the numerator. Add the terms inside the parentheses: 10 + 2 = 12. The numerator becomes 5 * 12.
Step 3: Simplify the denominator. Multiply 2 by 10 to get 20, then subtract 14: 20 - 14 = 6. The denominator becomes 6.
Step 4: Rewrite the expression with the simplified numerator and denominator: (5 * 12) / 6.
Step 5: Simplify the fraction by performing the multiplication in the numerator (5 * 12) and then dividing the result by the denominator (6).
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Algebraic Expressions
An algebraic expression is a mathematical phrase that can include numbers, variables, and operation symbols. In this case, the expression 5(x+2)/(2x-14) consists of a numerator and a denominator, where 'x' is a variable that can take on different values. Understanding how to manipulate and evaluate these expressions is fundamental in algebra.
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Introduction to Algebraic Expressions
Substitution
Substitution is the process of replacing a variable in an expression with a specific value. For the expression given, substituting x=10 means replacing every instance of 'x' with 10, allowing us to simplify and evaluate the expression. This step is crucial for finding the numerical value of the expression.
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Order of Operations
The order of operations is a set of rules that dictates the sequence in which calculations should be performed to ensure consistent results. Commonly remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction), applying these rules correctly is essential when evaluating expressions to avoid errors in calculations.
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