https://file.aiquickdraw.com/mathbot/file/1725668747420giplo3qg.jpg

The equation in the image appears to be:

\[
(23 - (-7)(-4))x + 37 = -12 - (9 + 13 \cdot (4 - 8))x
\]

I will now solve this step by step.

### Step 1: Simplify both sides
- On the left-hand side, simplify \(23 - (-7)(-4)\):
  \[
  (-7)(-4) = 28 \quad \text{so} \quad 23 - 28 = -5
  \]
  Thus, the left-hand side becomes:
  \[
  -5x + 37
  \]

- On the right-hand side, simplify \(13 \cdot (4 - 8)\):
  \[
  4 - 8 = -4 \quad \text{so} \quad 13 \cdot (-4) = -52
  \]
  Now simplify the right-hand side:
  \[
  9 - 52 = -43
  \]
  So the right-hand side becomes:
  \[
  -12 - (-43)x = -12 + 43x
  \]

### Step 2: Substitute the simplified expressions into the equation
Now the equation becomes:
\[
-5x + 37 = -12 + 43x
\]

### Step 3: Move all terms involving \(x\) to one side and constant terms to the other
Add \(5x\) to both sides:
\[
37 = -12 + 48x
\]
Now add \(12\) to both sides:
\[
49 = 48x
\]

### Step 4: Solve for \(x\)
\[
x = \frac{49}{48}
\]

So the solution is:
\[
x = \frac{49}{48}
\]

Would you like further details or have any questions? Here are some related problems:

1. How would the solution change if the right-hand side had a different constant?
2. Can you solve a similar equation where the constant term on the left side changes?
3. What happens when the sign of one of the terms in the equation changes?
4. How can you check your solution by substituting \(x\) back into the equation?
5. How does the method of simplifying and solving change if the equation involves fractions?

**Tip:** Always simplify expressions inside parentheses first before moving terms around.

(23 - (-7)(-4))x + 37 = -12 - (9 + 13(4 - 8))x

This page provides a step-by-step solution to the linear equation (23 - (-7)(-4))x + 37 = -12 - (9 + 13(4 - 8))x. The solution simplifies both sides of the equation, and solves for x using fundamental algebraic techniques. Suitable for students in Grades 8-10.

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