Which of the following values are solutions to the inequality minus, 8, minus, 6, x, is less than or equal to, 1, question mark−8−6x≤1?
I., minus, 8, II., 5, III., minus, 10
I.−8II.5III.−10

We are given the inequality:

\[
-8 - 6x \leq 1
\]

To determine which values of \( x \) (i.e., \( x = -8 \), \( x = 5 \), and \( x = -10 \)) satisfy the inequality, we'll solve the inequality step by step.

### Step 1: Solve the inequality for \( x \)

1. Add 8 to both sides to get rid of the constant term on the left-hand side:

\[
-8 - 6x + 8 \leq 1 + 8
\]
\[
-6x \leq 9
\]

2. Now, divide both sides by -6. Remember that when dividing or multiplying an inequality by a negative number, the direction of the inequality reverses:

\[
x \geq \frac{9}{-6}
\]
\[
x \geq -\frac{3}{2}
\]

Thus, the solution to the inequality is:

\[
x \geq -\frac{3}{2}
\]

### Step 2: Check the given values

- **I. \( x = -8 \):**
  
  \( -8 \) is less than \( -\frac{3}{2} \), so it **does not** satisfy the inequality.

- **II. \( x = 5 \):**

  \( 5 \) is greater than \( -\frac{3}{2} \), so it **does** satisfy the inequality.

- **III. \( x = -10 \):**

  \( -10 \) is less than \( -\frac{3}{2} \), so it **does not** satisfy the inequality.

### Conclusion:
The only solution is:
\[
\boxed{II. \ 5}
\]

Would you like any further details on this explanation?

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Here are 5 related questions:
1. How do you solve inequalities that involve dividing by negative numbers?
2. Can you explain why the inequality reverses when dividing by a negative number?
3. What is the difference between solving equations and inequalities?
4. How do you check if a value satisfies a given inequality?
5. How do you graph inequalities on a number line?

**Tip:** Always remember to reverse the inequality sign when multiplying or dividing by a negative number.

Which of the following values are solutions to the inequality −8−6x≤1? I.−8 II.5 III.−10

Learn how to solve the inequality −8−6x≤1 step-by-step, including when to reverse the inequality sign. Check if the values -8, 5, and -10 satisfy the inequality. This problem is perfect for students in Grades 8-10 and covers essential algebraic concepts.

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