In Exercises 103–104, use the graph of y = |4 - x| to solve each inequality.
|4 - x| ≥ 5

Key Concepts

Absolute Value Function

The absolute value function, denoted as |x|, represents the distance of x from zero on the number line, always yielding a non-negative result. In the context of the inequality |4 - x| ≥ 5, it indicates that the expression 4 - x can be either greater than or equal to 5 or less than or equal to -5, leading to two separate cases to solve.

Inequalities

Inequalities express a relationship where one side is not necessarily equal to the other, using symbols like ≥, ≤, >, and <. In this case, the inequality |4 - x| ≥ 5 requires finding the values of x that satisfy this condition, which involves determining the intervals where the absolute value expression meets or exceeds 5.

Graphing Absolute Value Functions

Graphing absolute value functions involves plotting the V-shaped graph that reflects the behavior of the function. The graph of y = |4 - x| has a vertex at (4, 0) and opens upwards, allowing us to visually identify the regions where the function's value is greater than or equal to 5, which corresponds to the solution of the inequality.