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Let's solve the inequality step-by-step.

The inequality given is:

\[
x - 9 \leq 8x + 5
\]

### Step 1: Isolate the variable on one side.
To move the terms involving \( x \) to one side, we can subtract \( x \) from both sides:

\[
-9 \leq 7x + 5
\]

### Step 2: Simplify the constant terms.
Now, subtract 5 from both sides to isolate the term with \( x \):

\[
-9 - 5 \leq 7x
\]

This simplifies to:

\[
-14 \leq 7x
\]

### Step 3: Solve for \( x \).
To isolate \( x \), divide both sides by 7:

\[
x \geq \frac{-14}{7}
\]

This simplifies to:

\[
x \geq -2
\]

### Step 4: Write the solution in interval notation.
Since \( x \geq -2 \), the solution set in interval notation is:

\[
[-2, \infty)
\]

### Final Answer:
The solution set is \([ -2, \infty )\).

Would you like more details or have any further questions?

Here are 5 related questions to deepen your understanding:
1. How do you solve inequalities when dividing or multiplying by a negative number?
2. What changes when solving a strict inequality (like \( < \) instead of \( \leq \))?
3. How do you graph the solution of \( x \geq -2 \) on a number line?
4. Can you explain the difference between interval notation and set-builder notation?
5. How would the solution change if the inequality were \( x - 9 > 8x + 5 \)?

**Tip:** Always reverse the inequality sign when multiplying or dividing both sides by a negative number!

Solve the inequality x - 9 ≤ 8x + 5 and write the solution set in interval notation.

Learn how to solve the inequality x - 9 ≤ 8x + 5 with a step-by-step solution. This problem covers key algebra concepts, including solving linear inequalities and representing solutions in interval notation. Suitable for students in Grades 7-9.

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