Can you guess which inequality symbol you will need just by looking at the graph?
|x|≥1.5
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 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 greater 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 - 1.5 and 1.5. To calculate the midpoint, we find the mean of these two values.
Mean=- 1.5+ 1.5/2=0
The midpoint a lies at 0 on the number line.
Distance
To find the distance b, calculate the difference between the midpoint and the endpoints.
1.5- 0&= 1.5
0-( -1.5)&= 1.5
The distance from the midpoint to the endpoints is 1.5.
Inequality
By substituting the distance b=1.5 and midpoint a= 0 into the inequality, we can form and simplify our absolute value inequality.
