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 the expression: \(4(-2) + \frac{2}{3}(9)\).
4. Simplify each term: calculate \(4 \times (-2)\) and \(\frac{2}{3} \times 9\) separately.
5. Add the simplified terms together and compare the result to \(6\) to check if the inequality holds true (i.e., if the left side is greater than or equal to \(6\)).