When graphing an , we need to create two . One of the inequalities is the same as the original but without the . The second inequality has both the symbol and the of the left-hand side changed.
∣y∣≥x⇒{y≥xy≤-x(I)(II)
Note that a pair of numbers
(x,y) satisfies the original inequality if it satisfies
either of the two inequalities. This means that the of our inequality will be the of the solution sets of the two inequalities.
∣y∣≥x⇔y≥x or y≤-x
We now have a to graph. Both of the inequalities are , so both lines are going to be solid. Let's start by graphing the for the first inequality.
We will use
(1,0) as the test point to determine which to shade.
y≥x⇒0≱1 ×
Since substituting the point made the inequality false, we will shade the region that does not contain it.
We will use the same process to graph the second inequality. Let's use the same test point,
(1,0), to determine which region to shade.
y≤-x⇒0≰-1 ×
Since substituting the point made the inequality false, we will once again shade the region that does not contain it.
The solution set of the given inequality is the union of all the shaded regions.