2(y + 2) + 3y = 6
Solving the Linear Equation: 2(y + 2) + 3y = 6
Understanding how to solve linear equations is a fundamental skill in algebra, essential for students, learners, and anyone wanting to strengthen their math foundation. One common type of equation encountered is in the form of a linear expression involving variables and constants—such as 2(y + 2) + 3y = 6.
This article breaks down the step-by-step process to solve this equation, explains the math concepts involved, and offers context on why mastering such equations matters.
What Is the Equation?
We begin with: 2(y + 2) + 3y = 6
This equation combines parentheses, variable terms, and constants. The goal is to find the value of y that makes the equation true.
Step-by-Step Solution
Step 1: Remove parentheses
Distribute the 2 across (y + 2): 2(y + 2) = 2y + 4
Now the equation becomes: 2y + 4 + 3y = 6
Step 2: Combine like terms
Combine the y terms: 2y + 3y = 5y
Now the equation is: 5y + 4 = 6
Step 3: Isolate the variable term
Subtract 4 from both sides: 5y + 4 – 4 = 6 – 4 5y = 2
Step 4: Solve for y
Divide both sides by 5: y = 2 ÷ 5 y = 0.4
Verification
Plug y = 0.4 back into the original equation: 2(0.4 + 2) + 3(0.4) = 2(2.4) + 1.2 = 4.8 + 1.2 = 6 ✅ The equation holds true.
Why Solving Linear Equations Matters
Linear equations like 2(y + 2) + 3y = 6 appear in real-world problems, including physics, economics, and engineering. Being able to:
- Simplify expressions
- Combine like terms
- Isolate variables
- Verify solutions
builds a strong foundation for more advanced math topics such as systems of equations, inequalities, and functions.
Practical Applications
- Budgeting: Calculating fixed and variable costs.
- Physics: Relating distance, rate, and time.
- Business: Determining break-even points.
Mastering these skills helps in logical thinking and problem-solving in everyday life.
Conclusion
The equation 2(y + 2) + 3y = 6 simplifies to y = 0.4 after clear algebraic manipulation. Understanding how to solve such equations empowers learners to tackle more complex math challenges confidently. Practice makes perfect—keep solving equations to sharpen your skills!
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