We are asked to find and graph the solution set for all possible values of x in the given inequality.
11≤|x-2|+4
Before we remove the absolute value we need to rearrange the inequality.
To find the solution set, we will create a compound inequality by removing the absolute value. In this case, the solution set contains the numbers that make the distance between x and 2 greater than or equal to 7 in the positive direction or in the negative direction.
x-2 ≥ 7 or x-2≤ -7
Let's isolate x in both of these cases before graphing the solution set.
This tells us that all values less than or equal to - 5 will satisfy the inequality.
Solution Set
The solution to this type of compound inequality is the combination of the solution sets.
First Solution Set:& x ≥ 9
Second Solution Set:& x ≤ - 5
Combined Solution Set:& x≤ - 5 or x≥ 9
Graph
The graph of this inequality includes all values less than or equal to - 5 or greater than or equal to - 9. We show this by keeping the endpoints closed.
