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ANSWER

1. 18 + (–25) =. –7. ANSWER. ANSWER. 23º F. ?. ?. 1. 4. 2. –. –. =. 2. 3. 2. 3. Warm-Up #1. ANSWER. 3. What is the difference between a daily low temperature of –5º F and a daily high temperature of 18º F ?. Real Numbers.

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ANSWER

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  1. 1. 18 + (–25) = –7 ANSWER ANSWER 23º F ? ? 1 4 2. – – = 2 3 2 3 Warm-Up #1 ANSWER 3.What is the difference between a daily low temperature of –5º F and a daily high temperature of 18º F ?

  2. Real Numbers Natural (Counting) numbers: N = {1, 2, 3, …} Whole numbers: W = {0, 1, 2, 3, …} Integers: Z = {0, 1, 2, 3, …} Rational Numbers: Any number that can be written as a fraction where the numerator and denominator are both integers and the denominator doesn’t equal zero Irrational Numbers: Any number that isn’t a rational number Real Numbers Rational Numbers Irrational Numbers Integers -5 -2 -1 Whole Numbers 0 Natural Numbers 1 2 3

  3. 5 Graph the real numbers – and 3 on a number line. 4 5 Note that –= –1.25. Use a calculator to approximate 3 to the nearest tenth: 4 3 1.7. (The symbol means is approximately equal to.) 5 So, graph – between –2 and –1, and graph 3 between 1 and 2, as shown on the number line below. 4 EXAMPLE 1 Graph real numbers on a number line SOLUTION

  4. 1 7 + 4 = 4 + 7 13 = 1 13 EXAMPLE 3 Identify properties of real numbers Identify the property that the statement illustrates. SOLUTION Commutative property of addition SOLUTION Inverse property of multiplication

  5. (2 3) 9 = 2 (3 9) 15 + 0 = 15 for Examples 3 and 4 GUIDED PRACTICE Identify the property that the statement illustrates. SOLUTION Associative property of multiplication. SOLUTION Identityproperty of addition.

  6. 4(5 + 25) = 4(5) + 4(25) 1 500 = 500 for Examples 3 and 4 GUIDED PRACTICE Identify the property that the statement illustrates. SOLUTION Distributive property. SOLUTION Identityproperty of multiplication.

  7. = (–5) (–5) (–5) (–5) (–5)4 = –(5 5 5 5) –54 EXAMPLE 1 Evaluate powers = 625 = –625

  8. EXAMPLE 2 Evaluate an algebraic expression Evaluate –4x2 – 6x + 11 when x = –3. = –4(–3)2– 6(–3) + 11 –4x2 – 6x + 11 Substitute –3 for x. = –4(9) – 6(–3) + 11 Evaluate power. = –36 + 18 + 11 Multiply. = –7 Add.

  9. 63 –26 for Examples 1, 2, and 3 GUIDED PRACTICE Evaluate the expression. SOLUTION 216 SOLUTION –64

  10. (–2)6 5x(x –2) when x = 6 for Examples 1, 2, and 3 GUIDED PRACTICE SOLUTION 64 SOLUTION 120

  11. 3y2 – 4y when y = – 2 (z + 3)3when z = 1 for Examples 1, 2, and 3 GUIDED PRACTICE SOLUTION 20 SOLUTION 64

  12. 8x + 3x 5p2 + p – 2p2 3(y + 2) – 4(y – 7) EXAMPLE 4 Simplify by combining like terms = (8 + 3)x Distributive property = 11x Add coefficients. = (5p2– 2p2) + p Group like terms. = 3p2 + p Combine like terms. = 3y + 6 – 4y + 28 Distributive property = (3y – 4y) + (6 + 28) Group like terms. = –y + 34 Combine like terms.

  13. 2x – 3y – 9x + y EXAMPLE 4 Simplify by combining like terms = (2x – 9x) + (– 3y + y) Group like terms. = –7x – 2y Combine like terms.

  14. for Example 5 GUIDED PRACTICE 8. Identify the terms, coefficients, like terms, and constant terms in the expression 2 + 5x – 6x2 + 7x – 3. Then simplify the expression. SOLUTION Terms: 2, 5x, –6x2 , 7x, –3 5 from 5x, –6 from –6x2 , 7 from 7x Coefficients: Like terms: 5x and 7x, 2 and –3 Constants: 2 and –3 Simplify: –6x2 +12x – 1

  15. 15m – 9m 2n – 1 + 6n + 5 for Example 5 GUIDED PRACTICE Simplify the expression. SOLUTION 6m SOLUTION 8n + 4

  16. 2q2 + q – 7q – 5q2 3p3 + 5p2–p3 for Example 5 GUIDED PRACTICE SOLUTION 2p3 + 5p2 SOLUTION –3q2– 6q

  17. –4y –x + 10x + y 8(x – 3) – 2(x + 6) for Example 5 GUIDED PRACTICE SOLUTION 6x – 36 SOLUTION 9x –3y

  18. Classwork 1.1/1.2 WS 1.1 (2-18 even) WS 1.2 (2-26 even)

  19. Homework 1.1/1.2 In the Practice Workbook: WS 1.1 (1-19 odd) WS 1.2 (1-21 odd)

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