Which of the following values are solutions to the inequality \( -2 \leq 9-4 x \) ? \[ \begin{array}{lll}\text { I. } 10 & \text { II. }-4 & \text { III. } 6\end{array} \]

To determine which of the values \( 10 \), \( -4 \), and \( 6 \) satisfy the inequality: \[ -2 \leq 9 - 4x \] let's solve the inequality step by step. 1. **Solve for \( x \):** \[ -2 \leq 9 - 4x \] Subtract 9 from both sides: \[ -2 - 9 \leq -4x \] \[ -11 \leq -4x \] Now, divide both sides by \( -4 \). **Remember** that dividing or multiplying both sides of an inequality by a negative number reverses the inequality sign: \[ \frac{-11}{-4} \geq x \] \[ \frac{11}{4} \geq x \quad \text{or} \quad x \leq 2.75 \] 2. **Check each value:** - **I. \( x = 10 \):** \[ 10 \leq 2.75 \quad \text{? No} \] \( 10 \) does **not** satisfy the inequality. - **II. \( x = -4 \):** \[ -4 \leq 2.75 \quad \text{? Yes} \] \( -4 \) **does** satisfy the inequality. - **III. \( x = 6 \):** \[ 6 \leq 2.75 \quad \text{? No} \] \( 6 \) does **not** satisfy the inequality. **Conclusion:** Only the value \( -4 \) satisfies the inequality. **Answer:** Only II. –4 is a solution to the inequality.