Solve for x: 3x - 7 = 2x + 5 – A Simple Algebraic Breakdown

Understanding how to solve algebraic equations like 3x - 7 = 2x + 5 is essential for mastering basic algebra. Whether you're a student, educator, or self-learner, figuring out equations step by step builds confidence and strengthens problem-solving skills.

In this article, we’ll walk through solving 3x - 7 = 2x + 5 clearly and concisely, explaining the logic behind each move.

Understanding the Context

What is the Equation?

We begin with:
3x - 7 = 2x + 5
This equation states that the expression on the left, 3x - 7, is equal to the expression on the right, 2x + 5. Our goal is to isolate variable x and find its value.

Solve for x: 3x - 7 = 2x + 5.

Key Insights

Step 1: Eliminate variables from both sides

To begin solving, subtract 2x from both sides to gather all variable terms on one side:
3x - 2x - 7 = 2x - 2x + 5
Simplify:
x - 7 = 5

Step 2: Isolate the variable

Next, add 7 to both sides to isolate x:
x - 7 + 7 = 5 + 7
Simplify:
x = 12

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Final Thoughts

Final Answer

✅ x = 12

Why This Equation Matters

Solving 3x - 7 = 2x + 5 is more than just plugging numbers—it teaches foundational algebraic reasoning. From analysis to problem-solving and beyond, isolating variables is key in fields like physics, economics, and computer science.

Summary of Steps

  1. Subtract 2x from both sides:
    3x - 2x - 7 = 2x - 2x + 5 → x - 7 = 5
  2. Add 7 to both sides:
    x - 7 + 7 = 5 + 7 → x = 12