We are asked to find and graph the solution set for all possible values of x in the given inequality.
|x-5|≥ 3
To do this, we will create a compound inequality by removing the absolute value. In this case, the solution set is any number that makes the distance between x and 5 greater than or equal to 3 in the positive direction or in the negative direction.
x-5 ≥ 3 or x-5≤ - 3
Let's isolate x in both of these cases before graphing the solution set.
The above tells us that all values less than or equal to 2 will satisfy the second inequality.
Solution Set
The solution to this type of compound inequality is the union of the solution sets.
First Solution Set:& x≥ 8
Second Solution Set:& x≤ 2
Combined Solution Set:& x≤ 2 or x≥ 8
Graph
The graph of this inequality includes all values less than or equal to 2 or greater than or equal to 8. We show this by keeping the endpoints closed.
