2y + 4 + 3y = 6 - Veritas Home Health
Solving the Equation: 2y + 4 + 3y = 6 Explained Step-by-Step
Solving the Equation: 2y + 4 + 3y = 6 Explained Step-by-Step
Understanding linear equations is a fundamental skill in algebra, and solving equations like 2y + 4 + 3y = 6 is a perfect starting point for beginners. In this SEO-optimized guide, we’ll walk you through how to solve the equation step-by-step, explain key algebraic concepts, and help you master similar problems efficiently.
Understanding the Context
Understanding the Equation
The equation:
2y + 4 + 3y = 6
At first glance, this equation combines like terms — a crucial first step in simplifying and solving linear expressions. Let’s break it down.
Step 1: Combine Like Terms
Key Insights
On the left-hand side, you have two terms with the variable y:
- 2y
- 3y
These like terms can be combined by adding their coefficients:
2y + 3y = 5y
The constant term is simply 4.
So the equation simplifies to:
5y + 4 = 6
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Step 2: Isolate the Variable Term
Next, subtract 4 from both sides of the equation to isolate the term with y:
5y + 4 – 4 = 6 – 4
→ 5y = 2
This step uses the fundamental algebraic principle that whatever operation you perform on one side, you must apply to both sides to maintain balance.
Step 3: Solve for y
Now, divide both sides by 5 to solve for y:
y = 2 ÷ 5
y = 0.4 (or 2⁄5 in fractional form)
