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: 89

Answer

False

Work Step by Step

The equation is false because the left side of the equation is not equal to the right side of the equation. The problem, as written, is: 3 + 7x = 10x It implies that the left side of the equation can be combined. This is FALSE. The terms on the left side of the equation cannot be combined. In algebra, only “like terms” may be added together or subtracted from one another. “Like terms” must have exactly the same variable parts. “3” and “7x” are the two terms in question. They do not have the same variable parts. One term, the “3” is called a constant term. It has no variable part. The other term, 7x, does have a variable part of “x.” The two terms are not like terms and cannot be combined. To make a true statement, we could use the equation: 3x + 7x = 10x. Then we do have like terms on the left side of the equation. Those terms: 3x and 7x can be combined. We do this by adding the numeric parts of 3 and 7. 3 + 7 = 10. Now we make sure to include the common variable part in our answer. So that 3x + 7x = 10x.
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