By Hardy G. H.

Hardy's natural arithmetic has been a vintage textbook on account that its ebook in1908. This reissue will carry it to the eye of a complete new iteration of mathematicians.

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2, 1), (0, 2), (4, 0) 2. (3, 1), (4, 4), (5, 8) 20. y = 2x − 1 and y = −2x + 2 3. (4, 1), (3, 2), (1, 3) 4. (1, 2), (2, 5), (4, 8) 21. y = 3x + 1 and y = − 13 x + 2 In exercises 5–10, find the slope of the line through the given points. 22. x + 2y = 1 and 2x + 4y = 3 5. (1, 2), (3, 6) 6. (1, 2), (3, 3) In exercises 23–26, find an equation of a line through the given point and (a) parallel to and (b) perpendicular to the given line. 7. (3, −6), (1, −1) 8. (1, −2), (−1, −3) 23. y = 2(x + 1) − 2 at (2, 1) 24.

Notice that the third number line indicates that the product is positive whenever x < −3 or x > 2. We write this in interval notation as (−∞, −3) ∪ (2, ∞). 1) x 2 + x − 6 > 0. 10 ϩ 2 No doubt, you will recall the following standard definition. 1 The absolute value of a real number x is |x| = x, −x, if x ≥ 0. 1 correctly. If x is negative, then −x is positive. This says that |x| ≥ 0 for all real numbers x. For instance, using the definition, |− 4 | = −(−4) = 4. Notice that for any real numbers a and b, |a · b| = |a| · |b|.

6, we show a graph of the polynomial on the left side of the inequality. 1) is equivalent to (x + 3)(x − 2) > 0. 2) xϩ3 Ϫ3 Ϫ x This can happen in only two ways: when both factors are positive or when both factors are negative. 3, we draw number lines for both of the individual factors, indicating where each is positive, negative or zero and use these to draw a number line representing the product. We show these in the margin. Notice that the third number line indicates that the product is positive whenever x < −3 or x > 2.