Let's solve the equation \( 50x - 10 = 8x + 16 \).

### Step 1: Move all terms involving \(x\) to one side.
Subtract \(8x\) from both sides:
\[
50x - 8x - 10 = 16
\]
\[
42x - 10 = 16
\]

### Step 2: Move constant terms to the other side.
Add \(10\) to both sides:
\[
42x = 16 + 10
\]
\[
42x = 26
\]

### Step 3: Solve for \(x\).
Divide both sides by 42:
\[
x = \frac{26}{42}
\]
Simplify the fraction:
\[
x = \frac{13}{21}
\]

So, the solution is \( x = \frac{13}{21} \).

Would you like more details or have any questions? 

Here are some related questions to expand on this:

1. How can you solve a system of linear equations involving two variables?
2. What happens when the equation has no solution or infinitely many solutions?
3. How would you solve the equation if it were quadratic instead of linear?
4. Can you explain how to check if your solution is correct by substitution?
5. What are some applications of solving linear equations in real life?

**Tip:** Always simplify fractions when solving equations for a cleaner result!

Learn how to solve the linear equation 50x - 10 = 8x + 16 with a detailed step-by-step solution. This problem involves key algebraic concepts like moving terms, simplifying fractions, and isolating the variable. Suitable for students in Grades 7-8.

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