We are asked to find and graph the solution set for all possible values of y in the given inequality.
|y|≥ 4.5
To do this, we will create a compound inequality by removing the absolute value. In this case, the solution set is any number with a distance greater than or equal to 4.5 away from the midpoint in the positive direction or a distance greater than or equal to 4.5 away from the midpoint in the negative direction.
y ≥ 4.5 or y≤ - 4.5
The first inequality tells us that all values greater than or equal to 4.5 will satisfy the inequality. The second inequality tells us that all values less than or equal to -4.5 will satisfy the inequality.
Solution Set
The solution to this type of compound inequality is the combination of the solution sets.
First Solution Set: & y≥ 4.5
Second Solution Set: & y≤ - 4.5
Combined Solution Set: & y≤ - 4.5 or y≥ 4.5
Graph
The graph of this inequality includes all values less than or equal to - 4.5 or greater than or equal to 4.5. We show this by keeping the endpoints closed.
