https://file.aiquickdraw.com/mathbot/file/17267157175287zf6y2kp.jpg

The problem in the image can be interpreted as two inequalities to solve:

1. \(-4x - 4 \leq 0\)
2. \(4x - 4 \leq 5\)

Let's solve each inequality step by step.

### 1. Solving \(-4x - 4 \leq 0\):

\[
-4x - 4 \leq 0
\]

Add 4 to both sides:

\[
-4x \leq 4
\]

Now, divide by \(-4\). Remember to reverse the inequality sign when dividing by a negative number:

\[
x \geq -1
\]

### 2. Solving \(4x - 4 \leq 5\):

\[
4x - 4 \leq 5
\]

Add 4 to both sides:

\[
4x \leq 9
\]

Now, divide by 4:

\[
x \leq \frac{9}{4}
\]

### Combined solution:

We now have the two inequalities:

\[
x \geq -1 \quad \text{and} \quad x \leq \frac{9}{4}
\]

The solution is the intersection of these two, which is:

\[
-1 \leq x \leq \frac{9}{4}
\]

This is the final solution.

---

Would you like more details or explanations? Here are some related questions to deepen understanding:

1. How do we solve compound inequalities?
2. Why does the inequality sign flip when dividing by a negative number?
3. What is the graphical representation of the solution \(-1 \leq x \leq \frac{9}{4}\)?
4. Can this solution be expressed in interval notation?
5. What is the difference between "and" and "or" in compound inequalities?

**Tip:** Always be careful when dividing inequalities by a negative number, as this changes the direction of the inequality.

Solve -4x - 4 ≤ 0 or 4x - 4 ≤ 5 and write the solution.

Learn how to solve the compound inequalities -4x - 4 ≤ 0 and 4x - 4 ≤ 5 with a detailed step-by-step solution. This problem covers key algebraic concepts, including solving linear inequalities and understanding inequality manipulation rules. Suitable for students in Grades 7-9.

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