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(D) To determine which inequality is satisfied by the interior points of the triangle,we check the vertices $(1, 3)$,$(5, 0)$,and $(-1, 2)$ for each i

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All the above

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(D) To determine which inequality is satisfied by the interior points of the triangle,we check the vertices $(1, 3)$,$(5, 0)$,and $(-1, 2)$ for each inequality.For $3x + 2y \ge 0$:$(1, 3) \implies 3(1) + 2(3) = 9 > 0$$(5, 0) \implies 3(5) + 2(0) = 15 > 0$$(-1, 2) \implies 3(-1) + 2(2) = 1 > 0$Since all vertices satisfy the inequality,the interior points also satisfy it.For $2x + y - 13 \le 0$:$(1, 3) \implies 2(1) + 3 - 13 = -8 \le 0$$(5, 0) \implies 2(5) + 0 - 13 = -3 \le 0$$(-1, 2) \implies 2(-1) + 2 - 13 = -13 \le 0$Since all vertices satisfy the inequality,the interior points also satisfy it.For $2x - 3y - 12 \le 0$:$(1, 3) \implies 2(1) - 3(3) - 12 = -19 \le 0$$(5, 0) \implies 2(5) - 3(0) - 12 = -2 \le 0$$(-1, 2) \implies 2(-1) - 3(2) - 12 = -20 \le 0$Since all vertices satisfy the inequality,the interior points also satisfy it.Therefore,all the given inequalities are satisfied.

All points lying inside the triangle formed by the points $(1, 3)$,$(5, 0)$,and $(-1, 2)$ satisfy which of the following inequalities?

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