Let's solve the equation step-by-step.

Given the equation:
\[
\frac{10}{4}y + \frac{8}{2} = 2y - 2
\]

First, simplify the fractions:
\[
\frac{10}{4}y = \frac{5}{2}y
\]
\[
\frac{8}{2} = 4
\]

So the equation becomes:
\[
\frac{5}{2}y + 4 = 2y - 2
\]

Next, let's isolate the variable \( y \). Start by getting all the \( y \) terms on one side and the constants on the other side. Subtract \( 2y \) from both sides:
\[
\frac{5}{2}y - 2y + 4 = -2
\]

Combine like terms. Convert \( 2y \) to a fraction with the same denominator as \(\frac{5}{2}y \):
\[
2y = \frac{4}{2}y
\]
\[
\frac{5}{2}y - \frac{4}{2}y + 4 = -2
\]
\[
\frac{1}{2}y + 4 = -2
\]

Subtract 4 from both sides:
\[
\frac{1}{2}y + 4 - 4 = -2 - 4
\]
\[
\frac{1}{2}y = -6
\]

Multiply both sides by 2 to solve for \( y \):
\[
y = -12
\]

So, the solution to the equation is:
\[
y = -12
\]

Would you like more details or have any questions?

Here are some related questions to further your understanding:
1. How do you solve equations involving fractions?
2. What steps are involved in isolating the variable in an equation?
3. Can you solve the equation \(3y/5 + 7 = y - 1\)?
4. What is the importance of common denominators in fraction operations?
5. How can you check your solution to ensure it is correct?

**Tip:** Always double-check your work by substituting your solution back into the original equation to verify its correctness.

Discover how to solve the linear equation 10/4(y) + 8/2 = 2y - 2. This solution involves simplifying fractions and isolating the variable step by step. Ideal for students in Grades 7-9 learning algebra and fractions.

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