Use a graphing utility to verify your solution sets to any three of the rational inequalities that you solved algebraically in Exercises 43–60.
Solve each rational inequality in Exercises 43–60 and graph the solution set on a real number line. Express each solution set in interval notation.
43.
45.
50.
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COLLEGE ALGEBRA ESSENTIALS
- In Exercises 11–12, find the solution set for each equation. 11. |5x + 3| = 7 12. |6x + 1| = [4x + 15||arrow_forwardExercises 105–107 will help you prepare for the material covered in the next section. 105. Let x represent a number. a. Write an equation in x that describes the following conditions: Four less than three times the number is 32. b. Solve the equation and determine the number. 106. Let x represent the number of countries in the world that are not free. The number of free countries exceeds the number of not-free countries by 44. Write an algebraic expression that represents the number of free countries. 107. You purchase a new car for $20,000. Each year the value of the car decreases by $2500. Write an algebraic expression that represents the car's value, in dollars, after x years.arrow_forwardq. Please solve and provide detail why does x+1, x<1 doesnot existarrow_forward
- x can be any real number between -6 and 3 or any real number greater than or equal to 25.arrow_forwardDetermine the largest subset of real numbers that is NOT a solution to the inequality (x+ 8)(x−7) > 0.arrow_forwardUse the graphs of the linear functions to solve Exercises 89–90. x + 3y = 12 x - 3y = -6 x - y = 4 x - 3y = 6 89. Write the linear system whose solution set is {(6, 2)}. Express each equation in the system in slope-intercept form.arrow_forward
- Find the interval notation of 19x+2>-18+3xarrow_forwardFind the interval (a, a + 1) for integer value a for which e 2x + 3 has a solution. Please select file(s) Select file(s)arrow_forwardMake Sense? In Exercises 115–118, determine whether each statement makes sense or does not make sense, and explain your reasoning. 115. I solved x - 2| = 5 by rewriting the equation as x - 2 = 5 or x + 2 = 5. 116. I solved |x – 2|> 5 by rewriting the inequality as -5 5. 117. Because the absolute value of any expression is never less than a negative number, I can immediately conclude that the inequality |2x - 5| - 9 < -4 has no solution. 118. I'll win the contest if I can complete the crossword puzzle in 20 minutes plus or minus 5 minutes, so my winning time, x, is modeled by |x – 20| < 5.arrow_forward
- 23. Solve. Write your solutions in interval form 2x - 7 x² +7x+12 9 <1arrow_forwardDetermine whether each ordered pair is a solution to the inequality 7x+6y<−7 (−5,1) (−9,6) (1,−5) (−10,1) (6,6)arrow_forwardExercises 86–88 will help you prepare for the material covered in the next section. If –9 is substituted for x in the equation 4x – 3 = 5x + 6, is the resulting statement true or false? Simplify: 13 – 3(x + 2). Зх + Simplify: 10(**1).arrow_forward
- Algebra: Structure And Method, Book 1AlgebraISBN:9780395977224Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. ColePublisher:McDougal Littell