Math Problem Statement

Solve the equation 3x + 2y = 12.

Solution

The image shows the equation:

3x+2y=123x + 2y = 12

It looks like the task involves solving the equation for one variable or rearranging it to isolate one of the variables. Let me know if you'd like to isolate yy or xx, or if there's another operation you want to perform with this equation. Here's the general process for isolating yy:

To solve for yy:

  1. Subtract 3x3x from both sides: 2y=123x2y = 12 - 3x
  2. Divide both sides by 2: y=123x2ory=632xy = \frac{12 - 3x}{2} \quad \text{or} \quad y = 6 - \frac{3}{2}x

Would you like further steps or explanations on this? Also, here are five related questions:

  1. How do you isolate xx instead of yy in the same equation?
  2. What does solving for yy represent graphically for this equation?
  3. How would you solve the equation if xx and yy both had fractions?
  4. What methods can you use to check your solution for correctness?
  5. How can this equation be used to model real-world problems?

Tip: Always perform the same operation on both sides of an equation to keep it balanced.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations

Formulas

Standard form of a linear equation: Ax + By = C
Isolating a variable: Subtraction and Division

Theorems

Linear equation solving methods

Suitable Grade Level

Grades 7-9