Question

How do you graph the inequality `|4 – v| <5`?

Answer 1

Interval fro -1 to 9 represents this inequality.
See explanation below.

Explanation:

First, draw a graph of `y=|4-v|`.
Then draw a horizontal line `y=5`.
All intervals of `v` where the graph of `y=|4-v|` is below the graph of `y=5` are the solution to this inequality and should be highlighted. These highlighted intervals represent graphically what inequality `|4-v| < 5` represents algebraically.

The graph of `y=|4-v|` can be obtained by following these steps:
1. Start with `y=v`
graph{x [-10, 10, -5, 5]}
2. Change it to `y=-v` by symmetrically reflecting relative to X-axis
graph{-x [-10, 10, -5, 5]}
3. Shift it up by 4 units to get `y=4-v`
graph{4-x [-10, 10, -5, 5]}
4. All parts of graph that lie below X-axis symmetrically reflect to the other side of X-axis to get `y=|4-v|`
graph{|4-x| [-10, 10, -5, 5]}

As seen from the graph, `y=|4-v|` is below level `y=5` in the interval from -1 to 9. This interval represent the solution to to the original inequality.