Explain how to solve the given type of problem.(a) Linear inequality: 2x 2 1(b) Nonlinear inequality: (x - 1)(x- 4) <0(c) Absolute value equation: | 2x – 5| = 7(d) Absolute value inequality: | 2x - 5| <7

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College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter1: Equations And Graphs

Section: Chapter Questions

Problem 20CC: Explain how to solve the given type of problem. (a) Linear inequality: 2x1 (b) Nonlinear inequality:...

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Describe the steps needed to solve a quadratic inequality algebraically.
To solve the nonlinear inequality x+1x20 , we first observe that the number, ____ and ____ are zeros of the numerator and denominator. These numbers divide the real line into three intervals. Complete the table. Do any of the endpoints fail to satisfy the inequality> If so, which one(s)? ____________.The solution of the inequality is __________________.
(a) To solve the equation 2x+1=x+4 graphically, we graph the functions f(x)= and g(x)= on the same set of axes and determine the values of x at which the graphs of f and g intersect Graph f and g below, and use the graphs to solve the equation. The solution is x= . (b) To solve the inequality 2x+1x+4 graphically. we graph the functions f(x)= and g(x)= on the same set of axes and find the values of x at which the graph of g is ___________(higher/lower) than the graph of f . From the graphs in part (a) we see that the solution of the inequality is the interval (_______, ________).
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Elena needs to earn at least $450 a week during her summer break to pay for college. She works two jobs. One as a swimming instructor that pays $9 an hour and the other as an intern in a genetics lab for $22.50 per hour. How many hours does Elena need to work at each job to earn at least $450 per week? (a) Let x be the number of hours she works teaching swimming and let y be the number of hours she works as an intern. Write an inequality that would model this situation. (b) Graph the inequality. (c) Find three ordered pairs (x, y) that would be solutions to the inequality. Then, explain what that means for Elena.

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Explain how to solve the given type of problem. (a) Linear inequality: 2x 2 1 (b) Nonlinear inequality: (x - 1)(x- 4) <0 (c) Absolute value equation: | 2x – 5| = 7 (d) Absolute value inequality: | 2x - 5| <7