Solve the inequality. Graph the solution set.
|x| + 7>9
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
• A. The solution is one or more intervals. The solution is
(Type your answer in interval notation. Simplify your answer. Use integers or fractions for any numbers in the expression.)
• B. There are only one or two solutions. The solution set is ____ { (Use a comma to separate answers as needed.)
• C. There is no solution.
To solve the inequality, we can subtract 7 from both sides to isolate the absolute value expression:
|x| > 9 - 7
|x| > 2
The inequality|x| > 2 means that the distance from the origin (0) is greater than 2 units. This can be interpreted as x being less than -2 or x being greater than 2.
Therefore, the solution set is B. The solution set is {x < -2 , x > 2}.