Given the linear inequality $4x+\frac{2}{3}y\ge 6$, determine if the following ordered pair is a solution to the inequality.
$(2,3)$

• A. Yes
• B. No
• C. Cannot be determined

Answer: (A)

Verified step by step guidance

1. Start with the given inequality: \(4x + \frac{2}{3}y \ge 6\).
2. Substitute the values of the ordered pair \((2, 3)\) into the inequality, replacing \(x\) with 2 and \(y\) with 3: \(4(2) + \frac{2}{3}(3) \ge 6\).
3. Simplify the expression by performing the multiplication: \(8 + 2 \ge 6\).
4. Add the terms on the left side: \(10 \ge 6\).
5. Since the inequality \(10 \ge 6\) is true, conclude that the ordered pair \((2, 3)\) is a solution to the inequality.