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

Jun 7, 2016

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.