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

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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.
Only $$ -4 $$ satisfies the inequality.

Which of the following values are solutions to the inequality ?

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