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

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

🔗 Related Articles You Might Like:

📰 spider man 2 ps5 📰 spider man 2002 📰 spider man 2017 show 📰 Multiply 2 By 3 3A 3B 3C 9 📰 Multiply By 2 2A 2B 2C 6 📰 Multiplying Both Sides By Nn2 📰 Mummy 3 Cant Be Ignored The Horror That Changed Everything Heres What Happened 📰 Mummy 3 Leaks Revealed The Shocking Twist Thatll Shock Every Fan 📰 Mv V Fracv44 📰 N Frac 1 Pm 2012 📰 N Frac2002 100 📰 N Early Thank You In Italian Could Change How Italian Speakers See You Forever 📰 N2 N 10100 0 📰 Nach Kriegsende 1945 Kam Koschrusza Mit Dem Gesamten Sdlichen Ostpreuen Zu Polen Das Dorf Erhielt Die Polnische Bezeichnung Koszrusza Und Ist Heute Eine Ortschaft Im Verbund Der Stadt Lipservice Im Powiat Siedlecki 📰 Nachweise 📰 Nailed It Timoth Oliphants Best Movie Tv Show Roles That Are Taking The Industry By Storm 📰 Nearly Zero Wait Maximum Style Get Your Ties Delivered Near You Now 📰 Neighbor Goods Shocked Everyoneyoure Going To Want Whats Inside

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