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

1 Answer
Zor Shekhtman
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.

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