The area of the region defined by the inequality 2|x| + 3|y-1| ≤ 6 is 12 square units
How to determine the area?
The inequality is given as:
2|x| + 3|y-1| ≤ 6
Next, we plot the inequality
From the graph of the inequality (see attachment), we have the following highlights:
- The shape is a rhombus
- The diagonals are 6 and 4 units
The area of a rhombus is:
A = 0.5 * d1 * d1
This gives
A = 0.5 * 6 * 4
Evaluate
A = 12
Hence, the area of the region is 12 square units
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