Solve for x: 3x - 7 = 2x + 5.
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.
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.
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
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
- Subtract 2x from both sides: 3x - 2x - 7 = 2x - 2x + 5 → x - 7 = 5
- Add 7 to both sides: x - 7 + 7 = 5 + 7 → x = 12
Further Practice and Tips
- Always perform the same operation on both sides to maintain equality.
- Keep the equation balanced—what you do to one side, do to the other.
- Practice similar equations, such as 5x + 2 = 3x - 4 or 2(x + 1) = 10, to reinforce your skills.
Conclusion
Solving 3x - 7 = 2x + 5 is a classic algebra exercise that demonstrates how to isolate a variable step-by-step. Start by moving like terms together, then isolate x, and verify your answer. With practice, equations become simple tools to uncover unknown values and solve real-world problems.
If you're looking to sharpen your algebra skills, mastering this method opens the door to mastering more advanced math!
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