Solve the equation 2x + 3 = 3x - 4. - Richter Guitar
How to Solve the Equation 2x + 3 = 3x - 4: A Step-by-Step Guide
How to Solve the Equation 2x + 3 = 3x - 4: A Step-by-Step Guide
Solving linear equations is a foundational skill in algebra, essential for students, educators, and anyone looking to sharpen their problem-solving abilities. One of the most common and classic types of problems you’ll encounter is when you need to solve equations like 2x + 3 = 3x - 4. In this article, we’ll walk you through how to solve this equation step-by-step, explain the reasoning behind each move, and show why this skill matters in real-world applications.
Understanding the Context
What Does the Equation Mean?
The equation 2x + 3 = 3x - 4 sets two expressions equal: on the left side, you have 2x + 3, and on the right side, 3x - 4. Our goal is to find the value of x that makes both sides equal — essentially, the point where they intersect.
Step-by-Step Solution
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Key Insights
Step 1: Identify the goal
We want to isolate x on one side. Choose either side; here, we’ll move all x terms to the right and constants to the left.
Start with the original equation:
2x + 3 = 3x - 4
Step 2: Eliminate x terms from one side
Subtract 2x from both sides to move all x terms to the right:
2x + 3 - 2x = 3x - 4 - 2x
Simplifies to:
3 = x - 4
Step 3: Eliminate the constant
Now, add 4 to both sides to isolate x:
3 + 4 = x - 4 + 4
This simplifies to:
7 = x
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✅ Final Answer
x = 7
Why This Method Works
This process relies on the balance principle in algebra: whatever operation you perform on one side of the equation, you must do to the other side to maintain equality. By subtracting 2x and adding 4, we systematically reduce complexity while preserving the truth of the equation.
Real-World Applications
Solving for x in equations like this appears in many practical scenarios:
- Finance: Calculating break-even points where cost equals revenue.
- Science: Determining variables in formulas (e.g., motion, concentration).
- Everyday life: Figuring out measurements, proportions, or rates.
Mastering these algebra basics prepares you for more advanced math, programming, and data analysis.
