Solve. Graph the solution set.
|2x - 7|≤11
Select the correct choice below and, if necessary, fill in the answer box within your choice.
• A. 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.)
B. 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 find the solution set for the inequality |2x - 7| ≤ 11, we can split it into two cases: 2x - 7 ≤ 11 and 2x - 7 ≥ -11.
Case 1: 2x - 7 ≤ 11
Adding 7 to both sides gives 2x ≤ 18
Dividing both sides by 2 gives x ≤ 9
Case 2: 2x - 7 ≥ -11
Adding 7 to both sides gives 2x ≥ -4
Dividing both sides by 2 gives x ≥ -2
Therefore, the solution set for the inequality is -2 ≤ x ≤ 9. Thus, the correct choice is A. The solution is one or more intervals. The solution is [-2, 9]