https://file.aiquickdraw.com/mathbot/file/1728403038992yeqg4jci.jpg

Let's solve the equation step by step:

The given equation is:

\[
-2(x + 4) + 3x = x - 8
\]

### Step 1: Distribute the \(-2\) to both terms inside the parentheses.

\[
-2(x + 4) = -2x - 8
\]

Now the equation becomes:

\[
-2x - 8 + 3x = x - 8
\]

### Step 2: Combine like terms on the left-hand side.

\[
(-2x + 3x) - 8 = x - 8
\]

This simplifies to:

\[
x - 8 = x - 8
\]

### Step 3: Analyze the equation.

At this point, the equation is \( x - 8 = x - 8 \), which is always true for all values of \(x\). This indicates that the equation is **true for all real numbers**.

### Conclusion:

The correct answer is:

**C. all real numbers**

---

Would you like any further clarification or details? Here are 5 related questions to consider:

1. What are some examples of equations that have no solution?
2. How do you recognize when an equation has infinitely many solutions?
3. Can you give an example of an equation with exactly one solution?
4. What is the difference between equations with all real solutions and no solutions?
5. How can this concept be applied in solving systems of equations?

**Tip:** Always simplify the equation as much as possible before determining if it has one solution, no solution, or infinitely many solutions.

Solve the equation -2(x + 4) + 3x = x - 8.

Learn how to solve the linear equation -2(x + 4) + 3x = x - 8 step by step. This problem teaches the use of the distributive property and leads to an equation that is true for all values of x, indicating infinitely many solutions. Suitable for students in Grades 7-9.

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