. Algebra solving-mgaf2e_accessible_02_01.pptx

. Algebra solving-mgaf2e_accessible_02_01.pptx

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  Slide - 1 Copyright© 2020 and 2016 Pearson Education, Inc. All Rights Reserved Interactive Algebra Foundations Chapter 2 Integers and Introduction to Solving Equations
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  Slide - 2 Copyright© 2020 and 2016 Pearson Education, Inc. All Rights Reserved Section 2.1 Introduction to Integers
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  Copyright © 2020and 2016 Pearson Education, Inc. All Rights Reserved Slide - 3 Objectives A. Represent Real-Life Situations with Integers. B. Graph Integers on a Number Line. C. Compare Integers. D. Find the Absolute Value of a Number. E. Find the Opposite of a Number. F. Read Bar Graphs Containing Integers.
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  Copyright © 2020and 2016 Pearson Education, Inc. All Rights Reserved Slide - 4 Positive and Negative Numbers Numbers greater than 0 are called positive numbers. Numbers less than 0 are called negative numbers.
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  Copyright © 2020and 2016 Pearson Education, Inc. All Rights Reserved Slide - 5 Negative and Positive Numbers −3 indicates “negative three.” 3 and + 3 both indicate “positive three.” The number 0 is neither positive nor negative.
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  Copyright © 2020and 2016 Pearson Education, Inc. All Rights Reserved Slide - 6 Example 1 The world’s deepest bat colony spends each winter in a New York zinc mine at a depth of 3805 feet. Represent this position with an integer. (Source: Guinness Book of World Records.) −3805
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  Copyright © 2020and 2016 Pearson Education, Inc. All Rights Reserved Slide - 7 Comparing Integers We compare integers just as we compare whole numbers. For any two numbers graphed on a number line, the number to the right is the greater number and the number to the left is the smaller number.  means “is less than”  means “is greater than”
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  Copyright © 2020and 2016 Pearson Education, Inc. All Rights Reserved Slide - 8 Graphs of Integers The graph of −5 is to the left of −3, so −5 is less than −3, written as −5 < −3. We can also write −3 > −5. Since −3 is to the right of −5, −3 is greater than −5.
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  Copyright © 2020and 2016 Pearson Education, Inc. All Rights Reserved Slide - 9 Example 3 Insert < or > between each pair of numbers to make a true statement. a. 6 3   b. 7 0 8   c. 3.6 4.2   
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  Copyright © 2020and 2016 Pearson Education, Inc. All Rights Reserved Slide - 10 Absolute Value The absolute value of a number is the number’s distance from 0 on the number line. The symbol for absolute value is .
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  Copyright © 2020and 2016 Pearson Education, Inc. All Rights Reserved Slide - 11 Example 4 Simplify. a. 8  = 8 because −8 is 8 units from 0. b. 9 = 9 because 9 is 9 units from 0. c. 15  = 15 because −15 is 15 units from 0.
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  Copyright © 2020and 2016 Pearson Education, Inc. All Rights Reserved Slide - 12 Helpful Hint (1 of 2) Since the absolute value of a number is that number’s distance from 0, the absolute value of a number is always 0 or positive. It is never negative.
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  Copyright © 2020and 2016 Pearson Education, Inc. All Rights Reserved Slide - 13 Opposite Numbers (1 of 2) Two numbers that are the same distance from 0 on the number line but are on the opposite sides of 0 are called opposites.
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  Copyright © 2020and 2016 Pearson Education, Inc. All Rights Reserved Slide - 14 Opposite Numbers (2 of 2) 5 is the opposite of −5 and −5 is the opposite of 5. The opposite of 4 is −4 is written as 4 (4)   The opposite of −4 is 4 is written as   4 4    If a is a number, then . ( )    a a
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  Copyright © 2020and 2016 Pearson Education, Inc. All Rights Reserved Slide - 15 Helpful Hint (2 of 2) Remember that 0 is neither positive nor negative. Therefore, the opposite of 0 is 0.
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  Copyright © 2020and 2016 Pearson Education, Inc. All Rights Reserved Slide - 16 Example 5 Find the opposite of each number. a. 14 The opposite of 14 is −14. b. −3 The opposite of −3 is ( ) 3 3.   or
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  Copyright © 2020and 2016 Pearson Education, Inc. All Rights Reserved Slide - 17 Example 6 Simplify. a. 5 ( )   The opposite of −5 is 5. b. 8   The opposite of the absolute value of −8 is the opposite of 8, or −8. c. 3  The opposite of the absolute value of 3 is the opposite of 3, or −3.
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  Copyright © 2020and 2016 Pearson Education, Inc. All Rights Reserved Slide - 18 Example 7 Evaluate  x if x = −6. Replace x with −6; then simplify. 6    x 6 
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  Copyright © 2020and 2016 Pearson Education, Inc. All Rights Reserved Slide - 19 Example 8 Which planet has the highest average daytime surface temperature? Venus Source: The World Almanac, 2009 * For some planets, the temperature given is the temperature where the atmospheric pressure equals 1 Earth atmosphere.