In Exercises 95–102, use interval notation to represent all values of x satisfying the given conditions.y = |2x - 5| + 1 and y > 9

An absolute value function, such as y = |2x - 5|, measures the distance of a number from zero on the number line, resulting in non-negative outputs. This function can create two cases based on the expression inside the absolute value: one where the expression is positive and another where it is negative. Understanding how to break down these cases is essential for solving inequalities involving absolute values.

Inequalities express a relationship where one side is not necessarily equal to the other, using symbols like '>', '<', '≥', or '≤'. In this context, the inequality y > 9 indicates that we are looking for values of x that make the output of the function exceed 9. Solving inequalities often involves finding critical points and testing intervals to determine where the inequality holds true.

Interval notation is a mathematical notation used to represent a range of values on the number line. It uses parentheses and brackets to indicate whether endpoints are included (closed intervals) or excluded (open intervals). For example, the interval (a, b) includes all numbers between a and b but not a and b themselves, while [a, b] includes both endpoints. This notation is crucial for succinctly expressing the solution set of inequalities.