https://file.aiquickdraw.com/mathbot/file/172687917641097dlc8a9.jpg

The equation in the image is:

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

We are asked to solve for \( y \). Let's go through the steps:

### Step 1: Expand the equation
Distribute the \( -3 \) to both \( y \) and \( 2 \):
\[
x - 3y - 6 = 6
\]

### Step 2: Isolate the \( y \)-term
Add 6 to both sides to isolate the \( y \)-term:
\[
x - 3y = 12
\]

### Step 3: Solve for \( y \)
Subtract \( x \) from both sides:
\[
-3y = 12 - x
\]

Now, divide both sides by \( -3 \):
\[
y = \frac{x - 12}{3}
\]

Thus, the solution for \( y \) is:
\[
y = \frac{x - 12}{3}
\]

Would you like further clarification or more details on any step?

Here are 5 related questions to consider:
1. How would the solution change if the constant on the right-hand side was different?
2. What happens if there are multiple variables in the equation?
3. Can this equation be solved graphically? How would you plot it?
4. How do you verify if the solution is correct by plugging back values for \( x \)?
5. What if you were solving for \( x \) instead of \( y \)?

**Tip:** Always perform distribution carefully to avoid mistakes when handling parentheses.

Solve each equation for y: x - 3(y + 2) = 6

Learn how to solve the linear equation x - 3(y + 2) = 6 for y. This example guides you through expanding the equation using distribution, isolating the variable y, and solving it. This problem is suitable for students in Grades 7-9, enhancing their skills in algebraic manipulation.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation