3a - 3(2) = 12 \Rightarrow 3a - 6 = 12 \Rightarrow 3a = 18 \Rightarrow a = 6
Solving 3a - 3(2) = 12: Step-by-Step Breakdown to Find a = 6
Understanding how to solve algebraic equations is essential for mastering math, whether you're a student learning the basics or someone brushing up on key concepts. One common equation you’ll encounter is:
3a - 3(2) = 12
This equation may look simple, but solving it correctly involves following logical algebraic steps to isolate the variable. In this article, we’ll break down the entire process clearly and show how it leads to the solution a = 6.
The Equation:
3a - 3(2) = 12
At first glance, this might seem straightforward, but understanding each step is key to grasping algebra.
Step 1: Simplify the Parentheses
Multiplication before subtraction is already completed here, so simplify 3(2):
3a - 6 = 12
This simplification reduces the equation to a clearer form: 3a - 6 = 12
Step 2: Add 6 to Both Sides
To isolate the term containing a, add 6 to both sides of the equation:
3a - 6 + 6 = 12 + 6 Simplifying both sides gives: 3a = 18
Now, the variable a is multiplied only by 3.
Step 3: Divide Both Sides by 3
To solve for a, divide both sides of the equation by 3:
3a ÷ 3 = 18 ÷ 3 This simplifies to: a = 6
Final Answer:
a = 6
Why this Matters
Mastering such equations builds the foundation for solving more complex expressions in algebra. Recognizing properties like the distributive law, order of operations, and inverse operations helps ensure accuracy in mathematical problem-solving. Whether used in academic settings, engineering, or finance, algebra remains a powerful tool.
By working through equations step-by-step—such as: 3a - 3(2) = 12 → 3a - 6 = 12 → 3a = 18 → a = 6—you reinforce key skills that enhance logical thinking and accuracy.
In summary: This simple equation demonstrates the importance of orderly step-by-step solving: simplifying, balancing both sides, and isolating the variable. Once mastered, this technique empowers students to tackle more advanced algebraic problems with confidence.
If you're learning algebra for school or personal growth, remember to practice like this—step-by-step, clearly, and with purpose.
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