For Exercises 13–18, solve the equation and related inequalities. (See Examples 2–3.)
a.
b.
c.
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- In Exercises 39–40, solve each linear inequality and graph the solution set on a number line. 39. 2(x + 3) > 6 – {4[x – (3x – 4) – x] + 4} - 40. 3(4x – 6) < 4 - {5x – [6x – (4x – (3x + 2))]}arrow_forwardGraph the equation. (Hint: Solve for x first.) x + 4 = 0 9- 16 3 (0.4) 2 13 1+ 1(4.0) - 4.0) 6-5- -7-6-5-4-3-2-1 12 3-4 5 6-7x -7-6-5-4-3-2-1-123-45 67x --7-6-5-4-3 123-456-7x -2 -3 (0,- 4) -6 4 0.2) (4.0) -7-6 -4-3-2-1 1 23-456 7x -2 -3 -4 **** ***** NO nA WN Harrow_forwardFor Exercises 21–54, solve the inequalities. (See Examples 1–2) 21. 4w? – 9N 0 22. 16z – 25 За 26. d? > 6d 27. 10 – 6x > 5x 28. 6 – 4x > 3x? 29. m? 0 34. (x + 2)(x + 5)(x – 4) 0 35. — 5c (с + 2)(4 - с) > 0 36. —би(и + 1)?(3— и) > 0 37. 14 10f + 9 0 - 42. -4x + 4x + 64x + 80x 2 0 43. —5и + 28и — 15и - 0 44. – 3w + 8w 4w -2 - 48. (4x + 1)? > -6 49. —4 2 (х — 7)° 50. —1 2 (х + 2)° 51. 16y > 24y - 9 52. 4w? > 20w – 25 53. (x + 3)(x + 1) < -1 54. (x + 2)(x + 4) < -1arrow_forward
- 2. A ball is thrown in the air. The relationship between the time the ball is in the air, t (in seconds), and the height of the ball in feet above the ground (h) is represented by h=-16t2 + 20t + 6 a. How many seconds will it take for the ball to reach it's maximum height? b. How many seconds will it take for the ball to hit the ground? c. Show your work to justify your answer. B I Σ Powered by Linklt! Hisense !!arrow_forward2. A rocket carrying fireworks is launched from a hill 80 feet above a lake. The rocket will fall into lake after exploding at its maximum height. The rocket's height above the surface of the lake is given by h = -16t² +64t + 80. a. b. C. d. What is the height of the rocket after 1.5 second? What is the maximum height reached by the rocket? How long will it take for the rocket to hit 128 feet the first time? brie (01) After how many seconds after it is launched will the rocket hit the lake? (08)arrow_forwardExample 2 Your turn Solve cach incquality. a. 3x- 3 <2(x+ 4) + x b. 4m + 3 55+ 4(m-3) 99+ re to search %2:arrow_forward
- For Exercises 47–60, solve the inequality, and write the solution set in interval notation if possible. (See Examples 6-7) 47. 3|4 – x| – 2 6 54. |12 - 7x| + 5 = 4 55. – 11 < 5 – |2p + 4| 56. – 18 < 6 – |3z + 3| 57. 10 < |-5c – 4| + 2 58. 15 <|-2d – 3|+ 6 y + 3 59. < 2 т — 4 60. < 14arrow_forward2. A rocket carrying fireworks is launched from a hill 80 feet above a lake. The rocket will fall into lake after exploding at its maximum height. The rocket's height above the surface of the lake is given by h = -16t² +64t + 80. a. b. C. d. What is the Co cket? After how many seconds after it is launched will the rocket hit the lake?arrow_forward15. Every year in Delaware there is a contest where people create cannons and catapults designed to launch pumpkins as far in the air as possible. The equation y = 10 + 95x- 16x- can be used to represent the height, y, of a launched pumpkin, where x is the time in seconds that the pumpkin has been in the air. What is the maximum height that the pumpkin reaches? How many seconds have passed when the pumpkin hits the ground? (Hint: If the pumpkin hits the ground, its height is 0 feet.) O The pumpkin's maximum height is 2.97 feet and it hits the ground after 6.04 seconds. O The pumpkin's maximum height is 151.02 feet and it hits the ground after 6.04 seconds. O The pumpkin's maximum height is 2.97 feet and it hits the ground after 151.02 seconds. O The pumpkin's maximum height is 151.02 feet and it hits the ground after 2.97 seconds.arrow_forward
- Exercise 2 Directions: Answer the following questions. Justify your answer by showing your solution. 1. Is-2 a solution of 4x +3= -5? 2. Is 3 a solution of 3x - 2 = -x - 4? 11 Is a solution of 5(x- 2) = 2x+1? 3. 3. 4. Is -1 a solution of 3x + 2 < -2? 5. Is a solution of 4x + 3 <-2? 4. LAPnli:eotion Outnutsarrow_forward6. (Solve by "Trial and Error".) Below is a floor plan of an art gallery. Is it possible to take a stroll that passes through EVERY doorway WITHOUT going through the same doorway twice? HOW?arrow_forwardFor Exercises 9–10, determine if the equation is linear or nonlinear. If the equation is linear, find the solution set. −2x = 8arrow_forward
- Big Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin Harcourt