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9. x2 5
14. x >
11.8<xs 10
13.-2sxs4
In Problems 15-18, write the given interval as an inequality.
15. [-7,9]
17. (-, 2)
16. [1, 15)
18. [-5, 0)
In Problems 19-34, solve the given linear inequality. Write the solution se
interval notation. Graph the solution set.
19.x +3 > -2
20. 3x- 9 < 6
22. 5 - x 2 -4
24. -(1 – x) > 2x – 1
26. -7x + 3<4 - x
21.x + 4 10
23.- x> x
25. 2 +x 2 3(x – 1)
MOORBBA
28. -3 < -x< 2
27-< x< 4
30. 3 < x + 4 < 10
32. 100 + x< 41 – 6x < 121 + x
3.
29. -7 <x - 2<1
31., 7 < 3 – įxs8
4х + 2
< 10
33. –1 s-4<}
34. 2 <
-3
4.
In Problems 35-58, solve the given nonlinear inequality. Write the solution set L
interval notation. Graph the solution set.
35. x² - 9 < 0
36. х — 16
38. 4x + 7x < 0
37. x(x – 5) N 0
39,x² – 8x + 12 < 0
41. 9x > 2x² – 18
43 (x + 1)(x – 2)(x – 4) < 0
45. (x² – 1)(x² – 4) < 0
40. (3x + 2)(x – 1) < 0
42. 4x > 9x + 9
44. (1 – x)(x +)(x – 3) <0
46. (x – 1)²(x + 3)(x – 5) =
47 5
x + 8
10
48.
х — 3
50.
49.
N-1
51.
+ 2 > 0
-
52.
x + 3
x(x - 1)
53.
(1 + x)(1 – x)
54. -
x +5
х
CHAPTER 1 INEQUALITIES, EQUATIONS, AND GRAPHS
expand button
Transcribed Image Text:9. x2 5 14. x > 11.8<xs 10 13.-2sxs4 In Problems 15-18, write the given interval as an inequality. 15. [-7,9] 17. (-, 2) 16. [1, 15) 18. [-5, 0) In Problems 19-34, solve the given linear inequality. Write the solution se interval notation. Graph the solution set. 19.x +3 > -2 20. 3x- 9 < 6 22. 5 - x 2 -4 24. -(1 – x) > 2x – 1 26. -7x + 3<4 - x 21.x + 4 10 23.- x> x 25. 2 +x 2 3(x – 1) MOORBBA 28. -3 < -x< 2 27-< x< 4 30. 3 < x + 4 < 10 32. 100 + x< 41 – 6x < 121 + x 3. 29. -7 <x - 2<1 31., 7 < 3 – įxs8 4х + 2 < 10 33. –1 s-4<} 34. 2 < -3 4. In Problems 35-58, solve the given nonlinear inequality. Write the solution set L interval notation. Graph the solution set. 35. x² - 9 < 0 36. х — 16 38. 4x + 7x < 0 37. x(x – 5) N 0 39,x² – 8x + 12 < 0 41. 9x > 2x² – 18 43 (x + 1)(x – 2)(x – 4) < 0 45. (x² – 1)(x² – 4) < 0 40. (3x + 2)(x – 1) < 0 42. 4x > 9x + 9 44. (1 – x)(x +)(x – 3) <0 46. (x – 1)²(x + 3)(x – 5) = 47 5 x + 8 10 48. х — 3 50. 49. N-1 51. + 2 > 0 - 52. x + 3 x(x - 1) 53. (1 + x)(1 – x) 54. - x +5 х CHAPTER 1 INEQUALITIES, EQUATIONS, AND GRAPHS
19. The points (-2, 0). (-2, 6), and (3, 0) are vertices of a rectangle. Find the
20. Describe the set of all points (x, r) in the coordinate plane. The set of all
In Problems 21-26, sketch the set of points (x, y) in the xy-plane whose coordin
ISIGNIA
fourth vertex.
points (x, -x).
Des Moines
22. ху > 0
24. x 2 and y 2-1
26. y 1
satisfy the given conditions.
%3D
23. x s1 and yl s2
25. x| > 4
Kansas
City
St. Lo
In Problems 27–32, find the distance between the given points.
28. A(-1, 3), B(5, 0)
30. A(-12, -3), B(-5, –7)
32. A(-3, 4), B(-3, -1)
27. A(1, 2), B(-3, 4)
29. A(2, 4), B(-4,-4)
31. A(-}, 1), B(}, -2)
FIGURE 1.3.15 Map f
In Problems 33-38, determine whether the points A, B, and C are vertices of atigh
'A
triangle, an isosceles triangle, or both.
34. A(-2, -1), B(8, 2), C(1, -11)
36. A(4, 0), B(1, 1), C(2, 3)
38. A(1, 1), B(4, 5), C(8, 8).
33. A(8, 1), B(-3, –1), C(10, 5)
35. A(2, 8), B(0, –3), C(6, 5)
37. A(-2, 1), B(0, 9), C(3, 4)
39. Suppose the points A(0, 0) and B(0, 6) are vertices of a triangle. Find a third
FIGURE 1.3.1
Problem 63
УА
vertex C so that the triangle is equilateral.
40. Find all points on the y-axis that are 5 units from the point (4, 4).
41. Consider the line segment joining the points A(-1, 2) and B(3, 4).
(a) Find an equation that expresses the fact that a point P(x, y) is equidistan
S-2MA speg
FIGURE
from A and from B.
Probler
(b) Describe geometrically the set of points described by the equation in nam.
42. Use the distance formula to determine whether the points A(-1, -5), B(2,4,
and C(4, 10) lie on a straight line.
010.-10.0.043. Find all points each with x-coordinate 6 such that the distance from each poim
(-1,2) is V85.
44. Which point, (1/V2, 1/V2) or (0.25, 0.97), is closer to the origin?
(-
In Problems 45 and 46, find all points P(x, x) that are the indicated distance fm
the given point.
(o
45. (-2, 0); V10
46. (3, –5); V34
In Problems 47–52, find the midpoint M of the line segment joining the poins
A and B.
1.
47. A(4, 1), B(-2, 4)
49. A(-1,0), B(-8, 5)
51. A(2a, 3b), B(4a, –6b)
48. A(}, 1), B(3. –3)
50. A(}, –}), B(-3, 1)
52. A(x, x), B(-x, x + 2)
In Problems 53-56, find the point B if M is the midpoint of the line segment joinm
points A and R.
expand button
Transcribed Image Text:19. The points (-2, 0). (-2, 6), and (3, 0) are vertices of a rectangle. Find the 20. Describe the set of all points (x, r) in the coordinate plane. The set of all In Problems 21-26, sketch the set of points (x, y) in the xy-plane whose coordin ISIGNIA fourth vertex. points (x, -x). Des Moines 22. ху > 0 24. x 2 and y 2-1 26. y 1 satisfy the given conditions. %3D 23. x s1 and yl s2 25. x| > 4 Kansas City St. Lo In Problems 27–32, find the distance between the given points. 28. A(-1, 3), B(5, 0) 30. A(-12, -3), B(-5, –7) 32. A(-3, 4), B(-3, -1) 27. A(1, 2), B(-3, 4) 29. A(2, 4), B(-4,-4) 31. A(-}, 1), B(}, -2) FIGURE 1.3.15 Map f In Problems 33-38, determine whether the points A, B, and C are vertices of atigh 'A triangle, an isosceles triangle, or both. 34. A(-2, -1), B(8, 2), C(1, -11) 36. A(4, 0), B(1, 1), C(2, 3) 38. A(1, 1), B(4, 5), C(8, 8). 33. A(8, 1), B(-3, –1), C(10, 5) 35. A(2, 8), B(0, –3), C(6, 5) 37. A(-2, 1), B(0, 9), C(3, 4) 39. Suppose the points A(0, 0) and B(0, 6) are vertices of a triangle. Find a third FIGURE 1.3.1 Problem 63 УА vertex C so that the triangle is equilateral. 40. Find all points on the y-axis that are 5 units from the point (4, 4). 41. Consider the line segment joining the points A(-1, 2) and B(3, 4). (a) Find an equation that expresses the fact that a point P(x, y) is equidistan S-2MA speg FIGURE from A and from B. Probler (b) Describe geometrically the set of points described by the equation in nam. 42. Use the distance formula to determine whether the points A(-1, -5), B(2,4, and C(4, 10) lie on a straight line. 010.-10.0.043. Find all points each with x-coordinate 6 such that the distance from each poim (-1,2) is V85. 44. Which point, (1/V2, 1/V2) or (0.25, 0.97), is closer to the origin? (- In Problems 45 and 46, find all points P(x, x) that are the indicated distance fm the given point. (o 45. (-2, 0); V10 46. (3, –5); V34 In Problems 47–52, find the midpoint M of the line segment joining the poins A and B. 1. 47. A(4, 1), B(-2, 4) 49. A(-1,0), B(-8, 5) 51. A(2a, 3b), B(4a, –6b) 48. A(}, 1), B(3. –3) 50. A(}, –}), B(-3, 1) 52. A(x, x), B(-x, x + 2) In Problems 53-56, find the point B if M is the midpoint of the line segment joinm points A and R.
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