The area enclosed by 2|x| + 3|y| ≤ 6 is
12 sq unit
The given inequality is equivalent to the following system of inequalities.
2x + 3y ≤ 6, when x ≥ 0, y ≥ 0
2x - 3y ≤ 6, when x ≥ 0, y ≤ 0
- 2x + 3y ≤ 6, when x ≤ 0, y ≥ 0
- 2x - 3y ≤ 6, when x ≤ 0, y ≤ 0
Combining these inequalities represents a rhombus with sides 2x±3y=6 and 2x±3y=−6
∴ Length of the diagonals is 6 nd 4 units along x - axis and y - axis
∴ The required area =12×6×4=12 sq units