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Answer:
We want to graph the inequality:
3x - 2y ≤ 6
The first step is to write this as a linear equation, to do it, we can isolate y in one side of the inequality.
3x ≤ 6 + 2y
3x - 6 ≤ 2y
(3/2)x - 6/2 ≤ y
(3/2)x - 3 ≤ y
or:
y ≥ (3/2)x - 3
Because we have the symbol ≥
The points on the line are solutions, then the first part is to graph the line:
y = (3/2)*x - 3
Next, we have:
y equal to or larger than (3/2)*x - 3
Then we need to shade all the region above that line.
The graph can be seen below.
we have
----> inequality 1
The solution of the inequality 1 is the shaded area below the solid red line
The solution is the region D and region C
-----> inequality 2
The solution of the inequality 2 is the shaded area above the solid blue line
The solution is the region B and region C
The solution of the system is the common area
so
The solution is the region C
see the attached figure
therefore
the answer is the option C
Region C
