area of region defined by |3x - 18| + |2y + 7| <= 3

[brightmind]

what is the area of the region defined by the inequality: |3x ? 18| + |2y + 7| ? 3 ?
i've been trying to graph the left side and the horizontal line y=3. Then shade the region below y=3 and calculate this area. But I stuck beacuse I cannot graph the left side. First , I omit the obsolute bars by deivide the region for them:
|3x-18|=3x-18 if x?6,
=-3x+18 if x?6
|2y+7|=2y+7 if y?-3.5
=-2y-7 if y?-3.5
I'm stuck because they have different variables, I cannot graph this!!!

 

[Denis]

viewtopic.php?f=9&t=12145

 

[stapel]

what is the area of the region defined by the inequality: |3x ? 18| + |2y + 7| ? 3 ?

Where is 3x - 18 > 0? On this interval, how does the inequality simplify? What three-part inequality does the resulting absolute-value inequality create? Graph the solution region.

Where is 3x - 18 < 0? On this interval, how does the inequality simplify? What three-part inequality does the resulting absolute-value inequality create? Graph the solution region.

What are the areas of the two triangles forming the two solution region? What then is the total area?

If you get stuck, please reply showing all of your work and reasoning so far.

Thank you!

Eliz.