The solution set of a linear equation is closely related to the solution set of a linear inequality. Work Exercises in order, to investigate this connection. Write answers in interval notation when appropriate.
Generalize your results from Exercises 105–107 by answering the questions that follow.
(a) What is the solution set of ax + b = 0 if a Z 0?
(b) Suppose a > 0. What are the solution sets of ax + b < 0 and ax + b > 0?
(c) Suppose a < 0. What are the solution sets of ax + b < 0 and ax + b > 0?
Reference:
105. The solution set of a linear equation is closely related to the solution set of a linear inequality. Work Exercises in order, to investigate this connection. Write answers in interval notation when appropriate.
Use the x-intercept method to find the solution set of 3.7x - 11.1 = 0. How many solutions are there? How many solutions are there to any linear equation in one variable?
106.The solution set of a linear equation is closely related to the solution set of a linear inequality. Work Exercises in order, to investigate this connection. Write answers in interval notation when appropriate.
The solution from Exercise 105 is sometimes called a boundary number. Find the solution sets of 3.7x - 11.1 < 0 and 3.7x - 11.1 > 0 . Explain why the boundary number is appropriate for the solution you found in Exercise 105.
107.The solution set of a linear equation is closely related to the solution set of a linear inequality. Work Exercises in order, to investigate this connection. Write answers in interval notation when appropriate.
Use the x-intercept method to find the solution set of the equation
-4x + 6 = 0
Then find the solution sets of the inequalities
-4x + 6 < 0 and -4x + 6 > 0.
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