Mastering Linear Equations: Solving 4x + 12 – 2x = 6x – 3 Step by Step

Understanding and solving linear equations is a fundamental skill in algebra, forming the backbone of more advanced math concepts. One common equation learners encounter is:

4x + 12 – 2x = 6x – 3
which simplifies to:
2x + 12 = 6x – 3

Understanding the Context

In this article, we’ll walk through how to solve this equation step-by-step and explain why each move correctly leads to isolating the variable. This classic problem not only reinforces algebraic reasoning but also prepares students for real-world applications, such as budgeting, speed calculations, and financial modeling.

Step 1: Simplify Both Sides

Start by combining like terms on each side of the equation.

4x + 12 - 2x = 6x - 3 \implies 2x + 12 = 6x - 3

Key Insights

Left side:
4x – 2x + 12 = 2x + 12

Right side: remains 6x – 3 (no further simplification needed)

Now the equation becomes:
2x + 12 = 6x – 3

Step 2: Move All Terms with x to One Side

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But this is not a standard form — perhaps simplify:
But \( 2\sqrt{30} \) is simplified.
Alternatively, compute the exact

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Final Thoughts

To isolate variable terms, subtract 2x from both sides:

2x + 12 – 2x = 6x – 3 – 2x

Left side simplifies to:
12

Right side becomes:
4x – 3

Now we have:
12 = 4x – 3

Step 3: Eliminate Constants to Isolate the x Term

Next, add 3 to both sides to eliminate the constant on the right:

12 + 3 = 4x – 3 + 3
Which simplifies to:
15 = 4x