Solve the inequality. Then graph the solution set.
x-6| <9
Select the correct choice below and, if necessary, fill in the answer box within your choice.
А.
The solution is one or more intervals. The solution is
Simplify your answer. Type your answer in interval notation. Use integers or fractions for any numbers in the expression.)
• В.
There are only one or two solutions. The solution set is {
(Type an integer or a fraction. Use a comma to separate answers as needed.)
• C. There is no solution.
To solve the inequality x - 6| < 9, we isolate the absolute value term by removing the absolute value sign and considering both cases of the expression inside the absolute value.
Case 1: (x - 6) < 9
Solving this inequality:
x - 6 < 9
x < 9 + 6
x < 15
Case 2: -(x - 6) < 9
Solving this inequality:
-x + 6 < 9
-x < 9 - 6
-x < 3
x > -3 (Dividing by -1, changes the inequality sign)
Combining both cases, we have:
x < 15 and x > -3
In interval notation, the solution is (-3, 15).
Therefore, the correct answer is А. The solution is one or more intervals. The solution is (-3, 15).