https://file.aiquickdraw.com/mathbot/file/172838079215064m2j11y.jpg

Let's go through the steps to solve the given expression:

The expression is:
\[
-0.75(-4x - 3) + 9x - 0.25
\]

### Step 1: Distribute \(-0.75\) over \((-4x - 3)\).
This means multiplying \(-0.75\) by both \(-4x\) and \(-3\).

\[
-0.75 \times (-4x) = 3x
\]
\[
-0.75 \times (-3) = 2.25
\]

So, after distribution, the expression becomes:
\[
3x + 2.25 + 9x - 0.25
\]

### Step 2: Combine like terms.
The like terms here are \(3x\) and \(9x\), as well as \(2.25\) and \(-0.25\).

\[
3x + 9x = 12x
\]
\[
2.25 - 0.25 = 2.00
\]

Now the expression becomes:
\[
12x + 2
\]

### Final Answer:
\[
12x + 2
\]

Would you like more details, or have any questions about this process?

Here are some follow-up questions to deepen your understanding:
1. What is the process of distributing negative numbers over parentheses?
2. How do you identify like terms in an expression?
3. What is the significance of combining like terms in algebra?
4. Can you explain why the distribution of \(-0.75\) to \(-4x - 3\) results in positive terms?
5. How would the expression change if \(-0.75\) were positive?

**Tip:** Always carefully distribute negative signs when simplifying expressions to avoid mistakes in signs!

Simplify the expression: -0.75(-4x - 3) + 9x - 0.25

Learn how to simplify the algebraic expression -0.75(-4x - 3) + 9x - 0.25 by distributing and combining like terms. This problem covers key algebraic concepts, including the distributive property and simplifying expressions, suitable for students in Grades 8-10.

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