Use inverse operations on each part of the inequality.
Inequality: x≥ 3 OR x≤-1
Graph:
Practice makes perfect
In order to solve the compound inequality, we need to isolate the x-variable in each simple inequality. Let's take a look at each inequality separately.
We can now graph the inequalities separately, and then find the union of the solution sets. Since x≥ 3 can be read as "x is greater than or equal to three," we will have a closed circle at three indicating that it is a solution. The numbers that are greater than three are to its right, so here is where we will shade.
The second inequality can be read as "x is less than or equal to negative one." This will have a closed circle at negative one. The numbers that are less than negative one are to its left, so here is where we will shade on the number line.
Finally, we can graph the union of the two simple inequalities by combining the graphs.
The solution set for the compound inequality includes all of the numbers in either one of the shaded regions. We can express this algebraically by recombining the simple inequalities.
x≥ 3 OR x≤-1
