Answer:
- y > x + 5
- y ≤ -2x + 16
- x ≥ 6
Step-by-step explanation:
We can define the unshaded region with 3 inequalities by creating inequality expressions for each line separately in relation to the unshaded region.
First, we can write an inequality for the dotted line. The fact that it's dotted means that the inequality will be > or < (as opposed to ≥ or ≤). Since the unshaded region is under the dotted line (and we don't want to include it), we will use >:
y > x + 5
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This is in the form:
y = mx + b
where m = slope and b = y-intercept.
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Next, we can write an inequality for the left line. It's a solid line, so it will either be ≥ or ≤. Since the unshaded area is above it, we will use ≤:
y ≤ -2x + 16
Finally, we can write an inequality for the right line. This is a vertical line, meaning it has a set x-value. Since the unshaded region is to the left of the line (and we don't want to include that), we will use ≥:
x ≥ 6
So, the 3 inequalities that define the unshaded region are:
y > x + 5
y ≤ -2x + 16
x ≥ 6
