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The problem shown in the image is:

**Solve the equation below. Show the steps that lead to the solution.**
\[
6(3x - 2) + x - 8 = 2(4x - 5)
\]

Let's break it down step by step:

### Step 1: Distribute the constants.
- On the left-hand side, distribute \(6\) to both \(3x\) and \(-2\):
  \[
  6(3x - 2) = 18x - 12
  \]
- On the right-hand side, distribute \(2\) to both \(4x\) and \(-5\):
  \[
  2(4x - 5) = 8x - 10
  \]

Now the equation becomes:
\[
18x - 12 + x - 8 = 8x - 10
\]

### Step 2: Combine like terms.
- On the left-hand side, combine \(18x\) and \(x\):
  \[
  18x + x = 19x
  \]
  Also, combine \(-12\) and \(-8\):
  \[
  -12 - 8 = -20
  \]

So the equation simplifies to:
\[
19x - 20 = 8x - 10
\]

### Step 3: Move all \(x\)-terms to one side and constants to the other.
- Subtract \(8x\) from both sides to get all \(x\)-terms on the left:
  \[
  19x - 8x - 20 = -10
  \]
  This simplifies to:
  \[
  11x - 20 = -10
  \]

- Add 20 to both sides to move constants to the right side:
  \[
  11x = -10 + 20
  \]
  Simplifying this gives:
  \[
  11x = 10
  \]

### Step 4: Solve for \(x\).
- Divide both sides by 11:
  \[
  x = \frac{10}{11}
  \]

### Final Answer:
\[
x = \frac{10}{11}
\]

Would you like more details on any step? 

Here are 5 related questions to deepen your understanding:
1. How do you handle equations with multiple parentheses and distribution?
2. What is the process for combining like terms in an equation?
3. Can you solve for \(x\) in other forms of linear equations?
4. How do you check if a solution to a linear equation is correct?
5. What are common mistakes when distributing terms in an equation?

**Tip:** Always distribute constants carefully before combining like terms to avoid errors when solving.

Solve the equation below. Show the steps that lead to the solution: 6(3x - 2) + x - 8 = 2(4x - 5).

Learn how to solve the linear equation 6(3x - 2) + x - 8 = 2(4x - 5) with detailed steps. This problem covers key algebraic concepts such as distribution, combining like terms, and solving for x. Suitable for students in Grades 8-10.

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