The solution set of a linear equation is closely related to the solution set of a linear inequality. Work Exercise in order to investigate this connection. Write answer in interval notation when appropriate.
Generalize your results from Exercises 119-121 by answering the questions that follow.
(a) What is the solution set of ax + b = 0 if a ≠ 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?
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 conditional linear equation in one variable?
The solution from Exercise 119 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 term boundary number is appropriate for the solution you found in Exercise 119.
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 conditional linear equation in one variable?
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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