The midpoint at 2 is at a distance of 3 from -1 and 5. Therefore, we can write the absolute value equation.
|x- 2|= 3
In order to write it as an absolute value inequality, we first notice in the graph that the endpoints are closed. This means that the inequality is non-strict. Since the solution set includes points that are farther away from the endpoints, the distance is greater than or equal to 3.
|x-2|≥3
Second Graph
Consider the given graph.
Since this graph has the same endpoints, the midpoint is also 2. We can write the same absolute value equation.
|x-2|=3
In order to write it as an absolute value inequality, we first notice in the graph that the endpoints are open. This means that the inequality is strict. Since the solution set includes points that are between the endpoints, the distance is less than 3.
|x-2|<3
Third Graph
Consider the given graph.
Since this graph has the same endpoints, the midpoint is also 2. We can write the same absolute value equation.
|x-2|=3
In order to write it as an absolute value inequality, we first notice in the graph that the endpoints are closed. This means that the inequality is non-strict. Since the solution set includes points that are between the endpoints, the distance is less than or equal to 3.
|x-2|≤ 3
Fourth Graph
Consider the given graph.
Since this graph has the same endpoints, the midpoint is also 2. We can write the same absolute value equation.
|x-2|=3
In order to write it as an absolute value inequality, we first notice in the graph that the endpoints are open. This means that the inequality is strict. Since the solution set includes points that are farther away from the endpoints, the distance is greater than 3.
|x-2|>3
