Solve the Equation: 3x – 4 = x + 5 – A Simple Algebraic Guide

Solving equations is a foundational skill in algebra, and one of the most common and helpful problems students face is 3x – 4 = x + 5. Whether you're a high school student, a self-learner, or a teacher, understanding how to solve linear equations like this is essential. In this article, we’ll walk through step-by-step instructions to solve 3x – 4 = x + 5, explore why it works, and share tips to master similar problems.

Understanding the Context

What Is the Equation 3x – 4 = x + 5?

The equation 3x – 4 = x + 5 is a linear equation involving a variable x on both sides. The goal is to isolate x on one side to find its value. Linear equations like this form the building blocks of algebra and are crucial for more advanced math such as systems of equations, graphing, and real-world problem solving.

Step-by-Step Solution

3x - 4 = x + 5

Key Insights

Here’s how to solve 3x – 4 = x + 5:

Step 1: Move all x terms to one side
Subtract x from both sides:
3x – 4 – x = x + 5 – x
This simplifies to:
2x – 4 = 5

Step 2: Isolate the constant terms
Add 4 to both sides to move the constant:
2x – 4 + 4 = 5 + 4
Which simplifies to:
2x = 9

Step 3: Solve for x
Divide both sides by 2:
2x ÷ 2 = 9 ÷ 2
x = 9/2 or 4.5

Continue Reading

s = \frac{9 + 12 + 15}{2} = 18
where \(15\) is the hypotenuse, calculated by \(c = \sqrt{9^2 + 12^2} = 15\). The radius \(r\) of the inscribed circle is given by:
r = \frac{A}{s} = \frac{54}{18} = 3

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Final Thoughts

Final Answer

➡️ x = 9⁄2
Or as a decimal:
➡️ x = 4.5

Why This Process Works

  • Subtracting or adding the same value to both sides keeps the equation balanced.
  • Moving like terms simplifies the expression and isolates the variable.
  • Dividing both sides by the coefficient of x leaves the solution unchanged and reveals x.

How to Use This Equation in Real Life

Solving equations like this is not just for school — it’s used every day in:

  • Budgeting (e.g., finding break-even points)
  • Physics (calculating motion, force, or energy)
  • Business analytics (revenue vs. cost comparisons)
  • Programming (logic for conditionals and loops)

Mastering such problems trains your logical thinking and prepares you for more complex concepts.