Solve the inequality. Then graph the solution set.
x-1| <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, we first split it into two separate inequalities:
1) x - 1 < 9
2) -(x - 1) < 9
For the first inequality:
x - 1 < 9
Adding 1 to both sides:
x < 10
For the second inequality:
-(x - 1) < 9
Expanding the inequality and multiplying by -1 (which flips the inequality):
-x + 1 < 9
Subtracting 1 from both sides:
-x < 8
Multiplying everything by -1 (which flips the inequality):
x > -8
Combining the solutions:
-8 < x < 10
Looking at the interval notation, the solution set is (-8, 10). Therefore, the correct choice is A. The solution is one or more intervals. The solution is (-8, 10).