Let's solve the inequality step by step:

### Given inequality:
\[
8 + 3(8c - 9) \leq 9c + 7 - 4c
\]

### Step 1: Expand the left-hand side.
Distribute the 3 across the terms inside the parentheses:
\[
8 + 3(8c - 9) = 8 + 24c - 27
\]
Simplifying this:
\[
8 - 27 + 24c = -19 + 24c
\]

Now the inequality looks like:
\[
-19 + 24c \leq 9c + 7 - 4c
\]

### Step 2: Simplify the right-hand side.
Combine like terms on the right-hand side:
\[
9c - 4c + 7 = 5c + 7
\]

So the inequality becomes:
\[
-19 + 24c \leq 5c + 7
\]

### Step 3: Move the terms with \(c\) to one side and constants to the other.
Subtract \(5c\) from both sides:
\[
-19 + 24c - 5c \leq 7
\]
This simplifies to:
\[
-19 + 19c \leq 7
\]

### Step 4: Isolate \(19c\).
Add 19 to both sides:
\[
19c \leq 7 + 19
\]
\[
19c \leq 26
\]

### Step 5: Solve for \(c\).
Divide both sides by 19:
\[
c \leq \frac{26}{19}
\]
Thus:
\[
c \leq \frac{26}{19}
\]

### Final Answer:
The solution is \(c \leq \frac{26}{19}\).

Would you like a more detailed explanation or have any questions?

Here are 5 related questions to expand on this:
1. How do you handle inequalities with negative coefficients?
2. Can you solve this inequality if it involves absolute values?
3. What happens if both sides of the inequality have fractions?
4. How would the solution change if you had a quadratic inequality?
5. What are the common mistakes when solving inequalities?

**Tip:** When multiplying or dividing by a negative number in an inequality, remember to reverse the inequality sign.

Solve the inequality 8 + 3(8c - 9) ≤ 9c + 7 - 4c step by step. This detailed explanation covers concepts such as the distributive property, combining like terms, and solving inequalities. Perfect for students in Grades 8-10.

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