Can you guess which inequality symbol you will need just by looking at the graph?
| x+1|≤ 4
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 closed. This means that our expression will be non-strict, either less than or equal to or greater than or equal to. Next, notice that the graph describes values that are less than or equal to 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 - 5 and 3. To calculate the midpoint, we find the mean of these two values.
Mean=- 5+ 3/2 ⇒ - 1
The midpoint a lies at - 1 on the number line.
Distance
To find the distance b, calculate the difference between the midpoint and the endpoints.
3-( - 1)&= 4
- 1-( - 5)&= 4
The distance from the midpoint to the endpoints is 4.
Inequality
By substituting the distance b= 4 and midpoint a= - 1 into the inequality, we can form and simplify our absolute value inequality.
