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We are given the inequality:

\[
8 + 3(8c - 9) \leq 9c + 7 - 4c
\]

### Step 1: Expand the terms on the left-hand side
Distribute the \(3\) across \((8c - 9)\):

\[
8 + 3(8c - 9) = 8 + 24c - 27
\]

Simplify the constants:

\[
8 - 27 = -19
\]

So the left-hand side becomes:

\[
24c - 19
\]

### Step 2: Simplify the right-hand side
Combine like terms on the right-hand side:

\[
9c - 4c = 5c
\]

So the inequality is now:

\[
24c - 19 \leq 5c + 7
\]

### Step 3: Isolate the variable \(c\)
Move all terms involving \(c\) to one side. First, subtract \(5c\) from both sides:

\[
24c - 5c - 19 \leq 7
\]

This simplifies to:

\[
19c - 19 \leq 7
\]

Next, add 19 to both sides:

\[
19c \leq 26
\]

### Step 4: Solve for \(c\)
Finally, divide both sides by 19:

\[
c \leq \frac{26}{19}
\]

So the solution is:

\[
c \leq \frac{26}{19}
\]

Would you like any additional details or clarification on the steps?

Here are 5 questions for further practice:
1. How would the inequality change if the coefficient of \(8c\) inside the parentheses was negative?
2. Can you solve a similar inequality: \(5 + 4(2x - 3) \leq 3x + 8 - x\)?
3. How would you handle a case where the inequality has fractions instead of whole numbers?
4. What happens to the inequality when multiplying or dividing by a negative number?
5. How would you graph the solution \(c \leq \frac{26}{19}\) on a number line?

**Tip:** Always simplify both sides of the inequality as much as possible before isolating the variable.

Solve the inequality: 8 + 3(8c - 9) ≤ 9c + 7 - 4c

Learn how to solve the inequality 8 + 3(8c - 9) ≤ 9c + 7 - 4c with a detailed step-by-step solution. This problem covers algebraic concepts such as distributive property, combining like terms, and isolating the variable. Suitable for students in Grades 8-10.

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