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

Understanding the Context

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.

3a - 3(2) = 12 \Rightarrow 3a - 6 = 12 \Rightarrow 3a = 18 \Rightarrow a = 6

Key Insights

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

Continue Reading

For \(x\) and \(y\) to be integers, \(a\) and \(b\) must both be even (since if both were odd, \(ab\) would be odd; if one odd and one even, \(a + b\) is odd). So both \(a\) and \(b\) must be even.
Let \(a = 2m\), \(b = 2n\), then \(4mn = 2024 \Rightarrow mn = 506\).
Now \(506 = 2 \cdot 11 \cdot 23\), so it has \((1+1)(1+1)(1+1) = 8\) positive divisors, giving 8 positive and 8 negative pairs \((m, n)\).

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Final Thoughts

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