Let's solve the equation step by step:

\[
0.6 + (0.5y - 1) = y + 0.5
\]

### Step 1: Simplify both sides
First, distribute and combine like terms:

\[
0.6 + 0.5y - 1 = y + 0.5
\]

Simplify the left side:

\[
(0.6 - 1) + 0.5y = y + 0.5
\]

\[
-0.4 + 0.5y = y + 0.5
\]

### Step 2: Move all terms involving \( y \) to one side and constant terms to the other
Subtract \( 0.5y \) from both sides:

\[
-0.4 = y - 0.5y + 0.5
\]

Simplify:

\[
-0.4 = 0.5y + 0.5
\]

### Step 3: Move constants to one side
Subtract \( 0.5 \) from both sides:

\[
-0.4 - 0.5 = 0.5y
\]

\[
-0.9 = 0.5y
\]

### Step 4: Solve for \( y \)
Divide both sides by \( 0.5 \):

\[
y = \frac{-0.9}{0.5}
\]

\[
y = -1.8
\]

Thus, the solution is:

\[
y = -1.8
\]

Would you like any further clarification or details on the steps? Here are five related questions:

1. How do you solve linear equations with parentheses?
2. What are some common strategies for solving equations involving fractions?
3. How do you check if a solution is correct for a given equation?
4. How does distributing work when solving linear equations?
5. How do you handle equations with variables on both sides?

**Tip:** Always simplify both sides of an equation first before trying to move terms around.

This page provides a step-by-step solution for solving the linear equation 0.6 + (0.5y - 1) = y + 0.5. Learn key algebraic techniques such as simplifying terms and isolating variables, suitable for students in Grades 6-8.

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