How do you solve and graph the inequality #abs(4 – v)< 5#?
2 Answers
Let's start from a graph of a function
For non-negative
For negative
That results in this graph of
graph{|x| [-10, 10, -5, 5]}
Now let's draw a graph of
According to principles of graph transformation, a graph of
graph{|x-4| [-10, 10, -5, 5]}
Now, to solve
Outside of this segment, that is if
For those interested in purely algebraic solution, here is how to do it.
Since, by definition,
we will consider two cases.
Case 1. Seeking solutions that satisfy the inequality
In this case
Solution to this is
Combined with the condition
Case 2. Seeking solutions that satisfy the inequality
In this case
Solution to this is
Combined with the condition
Now it's appropriate to combine two segments that represent the solutions of an original inequality into one segment since these segments are adjacent:
As you see, we get the same solution as using a graph above (which should not be a surprise).