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

Solve the equation 2x + 3 = 3x - 4.

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

Continue Reading

The altitude corresponding to a side is $ h = \frac{2A}{\text{side}} $. The longest altitude corresponds to the shortest side, which is 13 m:
h_{\text{longest}} = \frac{2 \cdot 84}{13} = \frac{168}{13} \approx 12.923
But we compute exactly:

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Final Thoughts

✅ 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.