https://file.aiquickdraw.com/mathbot/file/17273204715285rrkg1ff.jpg

The equation in the image appears to be:

\[
-2x - 5 = -4x + 12
\]

Let me solve it step by step:

### Step 1: Move all terms involving \(x\) to one side.
We can do this by adding \(4x\) to both sides:

\[
-2x + 4x - 5 = 12
\]

This simplifies to:

\[
2x - 5 = 12
\]

### Step 2: Move the constant to the other side.
Add 5 to both sides:

\[
2x = 17
\]

### Step 3: Solve for \(x\).
Divide both sides by 2:

\[
x = \frac{17}{2} \quad \text{or} \quad x = 8.5
\]

### Solution:
The value of \(x\) is \(8.5\).

Would you like more details or have any questions?

Here are 5 related questions for further exploration:
1. How would the solution change if the signs in the equation were reversed?
2. What happens if both sides of the equation were multiplied by a scalar?
3. How can we check if the solution \(x = 8.5\) is correct?
4. Can you graph this equation to visualize the solution?
5. How would you solve the equation if fractions were involved?

**Tip:** When moving terms in an equation, always perform the same operation on both sides to maintain equality.

Discover how to solve the linear equation -2x - 5 = -4x + 12 with a step-by-step guide. This example teaches key algebraic concepts such as equation balancing and solving linear equations. Suitable for students in Grades 8-10.

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