Mastering Linear Equations: Solving 4x + 12 โ€“ 2x = 6x โ€“ 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 โ€“ 2x = 6x โ€“ 3
which simplifies to:
2x + 12 = 6x โ€“ 3

Understanding the Context

In this article, weโ€™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.

Solved Question 10 Given: -2(3 - x) - 4 = 12 Prove: x= -11 | Chegg.com

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Solved Question 10 Given: -2(3 - x) - 4 = 12 Prove: x= -11 | Chegg.com
Solved (3xโˆ’6)โˆ’(x+2)=(3xโˆ’6)(โˆ’xโˆ’2)=โˆ’3x2โˆ’6x+6x+12=โˆ’3x2+12 If be | Chegg.com
Solved: 6x+4>2x+12 6x+2x>4+12 6x-2x>-4+12 [Math]
Solved (4x-6)2=(3x+10)2=(x+3)(x+9)=(4x-12y)(4x+12y)=(x+7)(x- | Chegg.com
Solved 11") K = (6x 12") L = 4x (3x- 3) - (x โ€“ 1) (2x 12x + | Chegg.com

Key Insights

Left side:
4x โ€“ 2x + 12 = 2x + 12

Right side: remains 6x โ€“ 3 (no further simplification needed)

Now the equation becomes:
2x + 12 = 6x โ€“ 3

Step 2: Move All Terms with x to One Side

Continue Reading

2z = 60^\circ + 360^\circ k \quad \text{ูˆ} \quad 2z = 120^\circ + 360^\circ k \quad \text{ู„ู€ } k \text{ ุนุฏุฏ ุตุญูŠุญ}
z = 30^\circ + 180^\circ k \quad \text{ูˆ} \quad z = 60^\circ + 180^\circ k
ู†ุญุชุงุฌ ุฅู„ู‰ ุฃู† ุชูƒูˆู† ุงู„ุฒูˆุงูŠุง ุถู…ู† $[0^\circ, 360^\circ]$. ู„ู€ $k = 0$:

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Final Thoughts

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

2x + 12 โ€“ 2x = 6x โ€“ 3 โ€“ 2x

Left side simplifies to:
12

Right side becomes:
4x โ€“ 3

Now we have:
12 = 4x โ€“ 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 โ€“ 3 + 3
Which simplifies to:
15 = 4x