Given the linear inequality $4x+\frac{2}{3}y\ge 6$, determine if the following ordered pair is a solution to the inequality.
$(0,9)$

• 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 \((0, 9)\) into the inequality, replacing \(x\) with \$0\( and \)y\( with \)9$.
3. This gives the expression: \(4(0) + \frac{2}{3}(9)\).
4. Simplify the expression by calculating \(4 \times 0\) and \(\frac{2}{3} \times 9\) separately.
5. Compare the simplified result to \$6$ to check if the inequality \(\ge 6\) holds true; if it does, the ordered pair is a solution, otherwise it is not.