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Guías de estudio > College Algebra

Solutions

Solutions to Try Its

1. [−3,5]\left[-3,5\right] 2. (−∞,−2)∪[3,∞)\left(-\infty ,-2\right)\cup \left[3,\infty \right) 3. x<1x<1 4. x≥−5x\ge -5 5. (2,∞)\left(2,\infty \right) 6. [−314,∞)\left[-\frac{3}{14},\infty \right) 7. 6<x≤9  or(6,9]6<x\le 9\text{ }\text{ }\text{or}\left(6,9\right] 8. (−18,12)\left(-\frac{1}{8},\frac{1}{2}\right) 9. ∣x−2∣≤3|x - 2|\le 3 10. k≤1k\le 1 or k≥7k\ge 7; in interval notation, this would be (−∞,1]∪[7,∞)\left(-\infty ,1\right]\cup \left[7,\infty \right). A coordinate plane with the x-axis ranging from -1 to 9 and the y-axis ranging from -3 to 8. The function y = -2|k 4| + 6 is graphed and everything above the function is shaded in.

Solutions to Odd-Numbered Exercises

1. When we divide both sides by a negative it changes the sign of both sides so the sense of the inequality sign changes. 3. (−∞,∞)\left(-\infty ,\infty \right) 5. We start by finding the x-intercept, or where the function = 0. Once we have that point, which is (3,0)\left(3,0\right), we graph to the right the straight line graph y=x−3y=x - 3, and then when we draw it to the left we plot positive y values, taking the absolute value of them. 7. (−∞,34]\left(-\infty ,\frac{3}{4}\right] 9. [−132,∞)\left[\frac{-13}{2},\infty \right) 11. (−∞,3)\left(-\infty ,3\right) 13. (−∞,−373]\left(-\infty ,-\frac{37}{3}\right] 15. All real numbers (−∞,∞)\left(-\infty ,\infty \right) 17. (−∞,−103)∪(4,∞)\left(-\infty ,\frac{-10}{3}\right)\cup \left(4,\infty \right) 19. (−∞,−4]∪[8,+∞)\left(-\infty ,-4\right]\cup \left[8,+\infty \right) 21. No solution 23. (−5,11)\left(-5,11\right) 25. [6,12]\left[6,12\right] 27. [−10,12]\left[-10,12\right] 29. x>−6 and x>−2Take the intersection of two sets.x>−2, (−2,+∞)\begin{array}{ll}x> -6\text{ and }x> -2\hfill & \text{Take the intersection of two sets}.\hfill \\ x>-2,\text{ }\left(-2,+\infty \right)\hfill & \hfill \end{array} 31. x<−3 or x≥1Take the union of the two sets.(−∞,−3)∪[1,∞)\begin{array}{ll}x< -3\text{ }\mathrm{or}\text{ }x\ge 1\hfill & \text{Take the union of the two sets}.\hfill \\ \left(-\infty ,-3\right){\cup }\left[1,\infty \right)\hfill & \hfill \end{array} 33. (−∞,−1)∪(3,∞)\left(-\infty ,-1\right)\cup \left(3,\infty \right) A coordinate plane where the x and y axes both range from -10 to 10. The function |x 1| is graphed and labeled along with the line y = 2. Along the x-axis there is an open circle at the point -1 with an arrow extending leftward from it. Also along the x-axis is an open circle at the point 3 with an arrow extending rightward from it. 35. [−11,−3]\left[-11,-3\right] A coordinate plane with the x-axis ranging from -14 to 10 and the y-axis ranging from -1 to 10. The function y = |x + 7| and the line y = 4 are graphed. On the x-axis theres a dot on the points -11 and -3 with a line connecting them. 37. It is never less than zero. No solution. A coordinate plane with the x and y axes ranging from -10 to 10. The function y = |x -2| and the line y = 0 are graphed. 39. Where the blue line is above the orange line; point of intersection is x=−3x=-3. (−∞,−3)\left(-\infty ,-3\right) A coordinate plane with the x and y axes ranging from -10 to 10. The lines y = x - 2 and y = 2x + 1 are graphed on the same axes. 41. Where the blue line is above the orange line; always. All real numbers. (−∞,−∞)\left(-\infty ,-\infty \right) A coordinate plane with the x and y axes ranging from -10 to 10. The lines y = x/2 +1 and y = x/2 5 are both graphed on the same axes. 43. (−1,3)\left(-1,3\right) 45. (−∞,4)\left(-\infty ,4\right) 47. {x∣x<6}\{x|x<6\} 49. {x∣−3≤x<5}\{x|-3\le x<5\} 51. (−2,1]\left(-2,1\right] 53. (−∞,4]\left(-\infty ,4\right] 55. Where the blue is below the orange; always. All real numbers. (−∞,+∞)\left(-\infty ,+\infty \right). A coordinate plane with the x and y axes ranging from -10 to 10. The function y = -0.5|x + 2| and the line y = 4 are graphed on the same axes. A line runs along the entire x-axis. 57. Where the blue is below the orange; (1,7)\left(1,7\right). A coordinate plane with the x and y axes ranging from -10 to 10. The function y = |x 4| and the line y = 3 are graphed on the same axes. Along the x-axis the points 1 and 7 have an open circle around them and a line connects the two. 59. x=2,−45x=2,\frac{-4}{5} 61. (−7,5]\left(-7,5\right] 63. 80≤T≤1201,600≤20T≤2,400\begin{array}{l}80\le T\le 120\\ 1,600\le 20T\le 2,400\end{array} [1,600,2,400]\left[1,600, 2,400\right]

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