Solve for x: 3x - 7 = 2x + 5. - Dachbleche24
Solve for x: 3x - 7 = 2x + 5 – A Simple Algebraic Breakdown
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.
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
🔗 Related Articles You Might Like:
📰 6a = 6 \times 12 = 72 📰 Therefore, the maximum possible erosion rate for any one region is \(\boxed{72}\). 📰 A hydrologist is modeling water flow through a system of aquifers. If the flow rates through three distinct aquifers are three consecutive integers, and their sum is 90 cubic meters per hour, what is the flow rate through the aquifer with the highest rate? 📰 Jackson William Murray 📰 Jacksonville Fl Zip Code 📰 Jacksonville Zip Code 📰 Jacktvtv 📰 Jaclyn Smith Kitchen Cabinet Color 📰 Jacob Black Black 📰 Jacob Black Twilight Family 📰 Jacob Black Twilight Saga 📰 Jacob Black Twilight 📰 Jacob Black 📰 Jacob Character In Twilight 📰 Jacob Elordi Beard 📰 Jacob Elordi Girlfriend 📰 Jacob Elordi Movies 📰 Jacob HopkinsFinal 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
- 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
