https://file.aiquickdraw.com/mathbot/file/1726446270072llxczjdn.jpg

The image shows the inequality:

\[
8 \leq -3x - 1
\]

Let's solve this step by step.

### Step 1: Isolate the term with \( x \)
We first add 1 to both sides of the inequality:
\[
8 + 1 \leq -3x
\]
\[
9 \leq -3x
\]

### Step 2: Solve for \( x \)
Now, we divide both sides by -3. Remember, when you divide or multiply an inequality by a negative number, the inequality sign reverses.

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

or equivalently:
\[
x \leq -3
\]

### Final Answer:
The solution to the inequality is:
\[
x \leq -3
\]

Would you like more details on the steps or explanations?

Here are 5 related questions:
1. How would the solution change if the inequality sign was a strict "<" instead of "≤"?
2. How can we represent the solution graphically on a number line?
3. What happens if we had \( +3x \) instead of \( -3x \) in the inequality?
4. Can this inequality be expressed in interval notation? If so, how?
5. How would this inequality be affected if it was an equation instead?

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

Learn how to solve the linear inequality 8 ≤ -3x - 1 step by step. This problem focuses on key algebraic concepts like isolating variables, applying inequality rules, and the effect of negative coefficients. Suitable for students in Grades 7-9.

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