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.