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 118
In Exercises 111–120, use the order of operations to simplify each expression. 6(−4)−5(−3)/(9−10)
Verified step by step guidance1
Identify the order of operations: Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). This is often remembered as PEMDAS.
Simplify the parentheses first. In this case, calculate \( 9 - 10 \), which simplifies to \( -1 \).
Next, handle the multiplication in the terms \( 6(-4) \) and \( -5(-3) \). Multiply \( 6 \) by \( -4 \) and \( -5 \) by \( -3 \).
Divide the result of \( -5(-3) \) by \( -1 \). Perform this division to simplify the fraction.
Finally, combine the results of \( 6(-4) \) and the simplified division from the previous step by performing the subtraction.
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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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Multiplication and Division
Multiplication and division are operations that are performed from left to right after addressing any parentheses or exponents in an expression. In the given problem, the multiplication of 6 and -4, as well as -5 and -3, must be calculated before any addition or subtraction occurs. Understanding how to handle these operations is essential for simplifying the expression accurately.
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Negative Numbers
Negative numbers are values less than zero and can affect the outcome of arithmetic operations. In this expression, the presence of negative numbers requires careful attention, especially when multiplying or dividing, as the rules for signs (positive times negative equals negative) must be applied. Recognizing how to work with negative values is vital for achieving the correct simplification.
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Related Practice
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Simplify each complex rational expression. (1/x-1/2)/(1/3-x/6)
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Textbook Question
Add or subtract as indicated. [(2x-7)/(x^2-9)]-[(x-10)/(x^2-9)]
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Add or subtract as indicated. 12/25x^2+11/15x^3
Textbook Question
In Exercises 111–120, use the order of operations to simplify each expression. 8−3[−2(2−5)−4(8−6)]
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