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. Calculate the left side of the inequality after substitution: \(4(-2) + \frac{2}{3}(9)\).
4. Simplify the expression step-by-step: first multiply \(4\) and \(-2\), then multiply \(\frac{2}{3}\) and \(9\).
5. Compare the simplified left side value to \(6\) to check if the inequality holds true (i.e., if the left side is greater than or equal to \(6\)). If it does, the ordered pair is a solution; if not, it is not a solution.