We are given the inequality:

\[
5y + 3 > -7y + 13
\]

Let's solve for \(y\):

### Step 1: Move all the terms involving \(y\) to one side of the inequality.
Add \(7y\) to both sides:

\[
5y + 7y + 3 > 13
\]

This simplifies to:

\[
12y + 3 > 13
\]

### Step 2: Move constant terms to the other side of the inequality.
Subtract 3 from both sides:

\[
12y > 10
\]

### Step 3: Solve for \(y\).
Divide both sides by 12:

\[
y > \frac{10}{12}
\]

Simplify the fraction:

\[
y > \frac{5}{6}
\]

Thus, the solution to the inequality is:

\[
y > \frac{5}{6}
\]

### Would you like more details or have any questions?

Here are 5 related questions:
1. How do you graph the solution \(y > \frac{5}{6}\) on a number line?
2. What changes if the inequality symbol is reversed, \(5y + 3 < -7y + 13\)?
3. Can you solve a similar inequality but with decimals, like \(2.5y + 1.2 > -3.7y + 5.6\)?
4. How does solving an equation differ from solving an inequality?
5. What happens to the inequality when multiplying or dividing by a negative number?

**Tip:** Always remember to reverse the inequality sign when multiplying or dividing both sides of an inequality by a negative number!

Learn how to solve the linear inequality 5y + 3 > -7y + 13 with a detailed, step-by-step guide. This problem covers key algebra concepts, including simplifying linear equations and solving inequalities. Perfect for students in Grades 7-9.

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