To solve the equation \( 2x + 3y = 12 \) for \( y \), we first isolate \( y \) in terms of \( x \).

### Steps:

1. Start with the equation:
   \[
   2x + 3y = 12
   \]
2. Subtract \( 2x \) from both sides to isolate the \( 3y \) term:
   \[
   3y = 12 - 2x
   \]
3. Now, divide both sides by 3 to solve for \( y \):
   \[
   y = \frac{12 - 2x}{3}
   \]
4. Simplify the expression:
   \[
   y = 4 - \frac{2x}{3}
   \]

So, the solution for \( y \) in terms of \( x \) is:
\[
y = 4 - \frac{2x}{3}
\]

Would you like more details or have any questions about the steps?

Here are 5 related questions to explore:

1. How would you solve \( y = 4 - \frac{2x}{3} \) if \( x = 3 \)?
2. What happens to \( y \) as \( x \) increases?
3. Can you graph the equation \( 2x + 3y = 12 \)?
4. How would you solve \( 2x + 3y = 12 \) for \( x \)?
5. What is the slope and intercept of the line represented by \( 2x + 3y = 12 \)?

**Tip**: When isolating a variable, always perform the same operations on both sides of the equation to maintain equality.

Learn how to solve the linear equation 2x + 3y = 12 for y in terms of x. This step-by-step solution involves isolating y, simplifying the expression, and understanding algebraic manipulation. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation