Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 6 - Algebra: Equations and Inequalities - 6.1 Algebraic Expressions and Formulas - Exercise Set 6.1: 91

Answer

True

Work Step by Step

The equation below is true because the left side of the equation is equivalent to the right side of the equation. (3y - 4) - (8y - 1) = -5y - 3 We can simplify the left side of the equation so that it matches the right side of the equation. Let’s start by focusing on the minus sign between the two sets of parentheses on the left side of the equation. This minus sign needs to be distributed across the entire second set of parenthesis on the left side of the equation. We distribute the minus sign just like we would a -1. We do this because the minus sign in front of an operation within parenthesis is the same as -1. Once we complete any distributive property, we can remove the parenthesis from it. The first set of parenthesis doesn’t have anything to be distributed, nor can we combine any like term, so we can remove those parentheses too. (It appears that they are to separate the two term from the rest of the equation. Completing the distribution of -1 across the second set of parenthesis, we get: 3y - 4 - 8y + 1 = -5y - 3 Explanation of the distribution: (-1)(8y) = -8y. And. (-1)(-1) = 1. Now, we can combine like terms on the left side of the equation. Keep in mind that the sign to the left of a term is “attached” to that term and works as a positive or negative when combining the terms. We have: 3y - 8y - 4 + 1 on the left side of the equation. I have rearranged the terms, keeping their signs with them so that all like terms are grouped together. We can combine like terms by adding or subtracting (as indicated). This gives us the following on the left side of the equation: 3y - 8y = -5y and -4 + 1 = -3, So the left side equals. -5y - 3 This now matches the right side of the equation. This tells us that we have a true statement/equation.
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