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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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 115
In Exercises 111–120, use the order of operations to simplify each expression. 8−3[−2(2−5)−4(8−6)]
Verified step by step guidance1
Step 1: Begin by simplifying the innermost parentheses. For the expression inside the first set of parentheses, calculate (2−5) and (8−6). This simplifies to −3 and 2, respectively.
Step 2: Substitute the simplified values back into the expression. The expression now becomes 8−3[−2(−3)−4(2)].
Step 3: Perform the multiplication inside the brackets. Multiply −2 by −3 to get 6, and multiply −4 by 2 to get −8. The expression now becomes 8−3[6−8].
Step 4: Simplify the subtraction inside the brackets. Calculate 6−8, which equals −2. The expression now becomes 8−3[−2].
Step 5: Perform the multiplication and subtraction outside the brackets. Multiply −3 by −2 to get 6, and then subtract this value from 8. The final simplified expression is obtained.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
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. The acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) helps remember this order. Following these rules is crucial for simplifying expressions correctly.
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Parentheses
Parentheses are used in mathematical expressions to indicate which operations should be performed first. When simplifying expressions, any calculations within parentheses must be completed before moving on to other operations. This ensures that the intended order of operations is respected and that the expression is simplified accurately.
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Distributive Property
The distributive property is a fundamental algebraic principle that states a(b + c) = ab + ac. It allows for the multiplication of a single term by each term within a set of parentheses. This property is essential when simplifying expressions that involve multiplication and addition or subtraction, as it helps break down complex expressions into simpler parts.
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Related Practice
Textbook Question
Add or subtract as indicated. [(2x-7)/(x^2-9)]-[(x-10)/(x^2-9)]
Textbook Question
In Exercises 111–114, simplify each expression. Assume that all variables represent positive numbers. (x−5/4y1/3x−3/4)−6
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Textbook Question
Add or subtract as indicated. 12/25x^2+11/15x^3
Textbook Question
In Exercises 107–114, simplify each exponential expression. Assume that variables represent nonzero real numbers. (2^−1x^−3y^−1)^−2(2x^−6y^4)^−2(9x^3y^−3)^0/(2x^−4y^−6)^2
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Textbook Question
Multiply or divide as indicated. [(x^2-5x-24)/(x^2-x-12)]/[(x^2-10x+16)/(x^2+x-6)]