To solve the equation \( 4x - 2 = 0.5x + 5 \), follow these steps:

1. **Move all terms involving \( x \) to one side:**
   \[
   4x - 0.5x = 5 + 2
   \]
   Simplifying the left side:
   \[
   3.5x = 7
   \]

2. **Solve for \( x \):**
   \[
   x = \frac{7}{3.5} = 2
   \]

So, the solution is \( x = 2 \).

Would you like details or have any questions? 

Here are some related questions:

1. What happens if you change the coefficients of \( x \) in the equation?
2. How do you solve an equation with fractions on both sides?
3. Can you solve a similar equation with a different constant on the right-hand side?
4. How do you verify the solution to a linear equation?
5. What if the equation had no solution? How would you identify that?

**Tip:** Always check your solution by substituting it back into the original equation.

Learn how to solve the linear equation 4x - 2 = 0.5x + 5 with a detailed step-by-step solution. This problem covers solving linear equations, a fundamental algebraic concept. Suitable for students in Grades 7-9.

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