Solving the Equation: 2(3) + 3r = 12

Understanding how to solve linear equations is fundamental in algebra and forms the basis for many advanced math applications. One such equation frequently studied is 2(3) + 3r = 12. While seemingly simple, mastering this equation helps build strong problem-solving skills. In this article, we’ll walk through the step-by-step process of solving 2(3) + 3r = 12, explain the algebra behind it, and highlight common pitfalls and best practices.

Understanding the Context

What Does the Equation 2(3) + 3r = 12 Mean?

The expression 2(3) + 3r = 12 combines constants, multiplication, and a variable, which alters how we approach solving for r. Parentheses must be evaluated first, followed by multiplication before addition or equating.

Step-by-Step Solution

2(3) + 3r = 12

Key Insights

Step 1: Evaluate the Multiplication Inside Parentheses

Start by simplifying the expression inside the parentheses: 

2(3) = 6

Now rewrite the equation: 

6 + 3r = 12
```

Step 2: Isolate the Variable Term


Subtract 6 from both sides to eliminate the constant on the left:

6 + 3r - 6 = 12 - 6
3r = 6

Step 3: Solve for r

Divide both sides by 3:
3r ÷ 3 = 6 ÷ 3
r = 2

Final Answer

r = 2

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Final Thoughts

Why This Equation Matters

While 2(3) + 3r = 12 is a basic linear equation, solving it introduces key algebraic concepts:

  • Order of operations: Parentheses before multiplication
  • Isolating variables: Moving constants to the opposite side
  • Balancing both sides: Maintaining equation integrity by performing identical operations

These skills are essential for solving more complex equations in algebra, such as those involving multiple variables or higher-degree polynomials.

Tips for Solving Similar Equations

  • Always simplify expressions inside parentheses first.
  • Perform multiplication or division before addition or subtraction.
  • Keep one side of the equation isolated at each step.
  • Check your answer by substituting r = 2 back into the original equation:
    2(3) + 3(2) = 6 + 6 = 12 ✔

Related Topics

  • Linear equations with one variable
  • Solving equations with coefficients
  • Algebraic expression simplification
  • Equation balancing techniques