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

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

Answer: (B)

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 \((-2, 9)\) into the inequality, replacing \(x\) with \(-2\) and \(y\) with \$9$.
3. This gives: \(4(-2) + \frac{2}{3}(9) \ge 6\).
4. Simplify each term: calculate \(4 \times (-2)\) and \(\frac{2}{3} \times 9\) separately.
5. After simplification, check if the resulting expression satisfies the inequality (i.e., if the left side is greater than or equal to 6).