4x + 12 - 2x = 6x - 3 \implies 2x + 12 = 6x - 3
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
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.
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
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
Step 4: Solve for x
Finally, divide both sides by 4 to solve for x:
x = 15 ÷ 4 x = 3.75
Why This Equation Matters
This algebraic process—combining like terms, moving variable terms, eliminating constants, and isolating the variable—is reusable across countless equation types. It builds critical thinking, logic, and precision, essential for STEM fields and everyday decision-making.
Summary
Solving 4x + 12 – 2x = 6x – 3 follows these clear steps:
- Simplify both sides
- Combine like terms
- Move variables to one side
- Eliminate constants
- Solve for x
Final answer: x = 3.75
Master this pattern, and you’ll unlock clearer reasoning in algebra and beyond!
Key takeaways:
- Always simplify both sides first
- Collect variable terms on one side
- Systematically move constants and isolate x
- Check your solution by substituting back
Start practicing with similar equations to build confidence—soon, linear equations won’t seem so daunting!
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