What is |11-2x|-6>11 in Set Notation?
To represent the inequality |11-2x| - 6 > 11 in set notation, we need to solve it step by step.
1. First, isolate the absolute value term by adding 6 to both sides of the inequality:
|11 - 2x| > 17
2. Break the inequality into two separate cases, one for when (11 - 2x) is positive and one for when it is negative:
(11 - 2x) > 17 or -(11 - 2x) > 17
3. Solve the first case:
11 - 2x > 17
Subtract 11 from both sides:
-2x > 6
Divide both sides by -2, remembering to reverse the inequality:
x < -3
4. Solve the second case:
-(11 - 2x) > 17
Distribute the negative sign:
-11 + 2x > 17
Add 11 to both sides:
2x > 28
Divide both sides by 2:
x > 14
5. Combine the solutions from the two cases:
x < -3 or x > 14
In set notation, the solution to the inequality is represented as an interval or union of intervals. We can write it as:
(-∞, -3) ∪ (14, +∞)
This represents all the values of x that make the inequality |11 - 2x| - 6 > 11 true.