Can you guess which inequality symbol you will need just by looking at the graph?
|x-5.5|>4.5
Practice makes perfect
An absolute valueinequality describes a distance b from a midpoint a, and can be written in a specific format.
|x- a| b
Let's examine the graph to fill in the missing pieces.
Immediately, we see that the endpoints are open. This means that our expression will be strict, either less than or greater than. Next, notice that the graph describes values that are greater than some distance from a midpoint.
|x- a| > b
Now, let's find our midpoint a and the distance b to complete the expression.
Midpoint
We can tell from the graph that the endpoints are 1 and 10. To calculate the midpoint, we find the mean of these two values.
Mean=1+ 10/2 ⇒ 5.5
The midpoint a lies at 5.5 on the number line.
Distance
To find the distance b, calculate the difference between the midpoint and the endpoints.
10- 5.5&= 4.5
5.5- 1&= 4.5
The distance from the midpoint to the endpoints is 4.5.
Inequality
By substituting the distance b= 4.5 and midpoint a= 5.5 into the inequality, we can form and simplify our absolute value inequality.
