By Charles P. McKeague (Auth.)
Quite transparent and obtainable, Pat McKeague's best-selling texts provide the entire assessment, drill, and perform scholars have to boost good mathematical skillability and self belief. McKeague's realization to element, extraordinary writing type, and association of mathematical techniques make instructing relaxing and studying obtainable. The 7th version of this renowned sequence supplies the publication a better emphasis at the connections among equations, tables, and graphs and by way of incorporating pedagogy that addresses collaborative studying and terminology
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Example text
For example, the number 5 is a term, as are the expressions 3x, — 7y, and I5xy. 1 Simplifying Expressions 45 46 Chapter 2 Linear Equations and Inequalities DEFINITION TWO or more terms with the same variable part are called similar (or like) terms. The terms 3x and 4x are similar since their variable parts are identical. Likewise, the terms 18j>, —lOj^, and 6y are similar terms. To simplify an algebraic expression, we simply reduce the number of terms in the expression. We accomplish this by applying the distributive property along with our knowledge of addition and subtraction of positive and negative real numbers.
List List List List all all all all the integers. the rational numbers. irrational numbers. real numbers. For each expression on the left list the letter(s) that justify the property used. 26. (x + y) + z = x + (z + y) A. Commutative property 27. 3(x - 5) = 3x - 15 of addition 28. a(3 · b) = 3(0 · b) B. Commutative property of multiplication Chapter 1 Test 44 Chapter 1 The Basics 29. 30. 31. (x + 5) + 7 = 7 + (x + 5) 3 · 5 - 4 · 5 = (3 - 4)5 (8 + x)5 = 5(8 + x) C. Associative property of addition D.
3[5 + (-5)] = -3(0) = 0 The answer is zero. We can also work the problem using the distributive property. -3[5 + (-5)] = -3(5) + (-3X-5) Distributive property ? = -15 + Since the answer to the problem is 0, our ? must be +15. (What else could we add to - 1 5 to get 0? ) We will do another example like this one later. Let us first summarize our results so far and look for similarities between the signs of the numbers in the problem and the answers we get. Original numbers have the same signs different signs different signs the same signs The answer is 3(5) 3(-5) -3(5) -3(-5) = = = = 15 -15 -15 15 positive negative negative positive Here are more examples involving repeated addition and the commutative property.