https://file.aiquickdraw.com/mathbot/file/17289537359095ny5qtdb.jpg

The equation provided in the image is:

\[
2(x - 10) - 6 = 16x - 82
\]

### Step-by-step solution:

1. **Distribute the 2 on the left-hand side**:
   \[
   2(x - 10) = 2x - 20
   \]
   So the equation becomes:
   \[
   2x - 20 - 6 = 16x - 82
   \]

2. **Simplify the left-hand side**:
   \[
   2x - 26 = 16x - 82
   \]

3. **Move all the terms with \(x\) to one side and constant terms to the other**. First, subtract \(2x\) from both sides:
   \[
   -26 = 14x - 82
   \]

4. **Add 82 to both sides**:
   \[
   56 = 14x
   \]

5. **Solve for \(x\)** by dividing both sides by 14:
   \[
   x = \frac{56}{14} = 4
   \]

### Final answer:
The solution is \(x = 4\).

Would you like any more details or explanations? Here are some related questions to explore further:

1. How do you solve linear equations with distribution?
2. What does it mean for an equation to have one solution?
3. How do you check if your solution to an equation is correct?
4. Can equations have no solution or infinite solutions?
5. How does moving terms across the equation work when solving?

**Tip:** Always simplify both sides of the equation before trying to isolate the variable.

Solve the equation: 2(x - 10) - 6 = 16x - 82

Learn how to solve the linear equation 2(x - 10) - 6 = 16x - 82 with a detailed step-by-step guide. This problem covers algebraic concepts, such as distribution, moving variables, and properties of equality. Suitable for students in Grades 8-10.

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