We are asked to find the solution set for all possible values of x in the given inequality.
|x-3|≥ 7
To do this, 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 3 greater than or equal to 7 in the positive direction or in the negative direction.
x-3 ≥ 7 or x-3≤ - 7
Let's isolate x in both of these cases.
This inequality tells us that all values less than or equal to - 4 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≥ 10
Second Solution Set:& x≤ - 4
Combined Solution Set:& x≤ - 4 or x≥ 10
