2(3) + 3r = 12

February 22, 2026

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.

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

Step 1: Evaluate the Multiplication Inside Parentheses

Start by simplifying the expression inside the parentheses:

Step 2: Isolate the Variable Term

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

Step 3: Solve for r

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

Final Answer

r = 2

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 ✔

Conclusion

The equation 2(3) + 3r = 12 might look simple, but it exemplifies core algebraic techniques. Whether you’re a student learning algebra basics or a parent supporting math education at home, understanding how to solve such equations strengthens your foundation for future math success. Practice creates mastery—so keep solving, checking, and growing your algebraic skills!

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