https://file.aiquickdraw.com/mathbot/file/1728472348051ha0k059o.jpg

The equation shown in the image is:

\[
6(y + 7) = 2(y - 3)
\]

Let's solve it step by step.

### Step 1: Distribute the numbers on both sides.

On the left-hand side:
\[
6(y + 7) = 6y + 42
\]

On the right-hand side:
\[
2(y - 3) = 2y - 6
\]

So now, the equation becomes:
\[
6y + 42 = 2y - 6
\]

### Step 2: Move all terms with \(y\) to one side and constants to the other side.

First, subtract \(2y\) from both sides:
\[
6y - 2y + 42 = -6
\]
This simplifies to:
\[
4y + 42 = -6
\]

### Step 3: Isolate the \(y\)-term.

Now, subtract 42 from both sides:
\[
4y = -6 - 42
\]
\[
4y = -48
\]

### Step 4: Solve for \(y\).

Finally, divide both sides by 4:
\[
y = \frac{-48}{4} = -12
\]

### Solution:
\[
y = -12
\]

Would you like any further explanation or details?

Here are some related questions to explore:
1. What happens when you check your solution by plugging \(y = -12\) into the original equation?
2. How do you solve equations with variables on both sides in general?
3. What would change if the constants were different in this equation?
4. Can equations like this have no solution or infinite solutions?
5. What are some practical applications of equations with variables on both sides?

**Tip:** Always check your solution by substituting it back into the original equation to make sure it satisfies both sides.

Learn how to solve the linear equation 6(y + 7) = 2(y - 3) using distributive property and combining like terms. This problem is ideal for students in Grades 7-8, covering essential algebraic concepts.

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