The inequality |2x-3| - 9 > 10 can be solved by considering the two cases of the absolute value expression, leading to two linear inequalities. Solving these inequalities provides the solution in interval notation: (-∞, -8) U (11, ∞), where x can be any number less than -8 or greater than 11.
To solve the inequality |2x-3| - 9 > 10, we first simplify the inequality to isolate the absolute value expression:
|2x-3| > 19
This leads to two separate cases since an absolute value expression represents the distance from zero and can be either positive or negative:
- 2x - 3 > 19
- 2x - 3 < -19
Solving each of these gives us:
In interval notation, the solution is:
(-∞, -8) U (11, +∞)
This means x can be any number less than -8 or greater than 11.