3x - 4 = x + 5 - United Radiology

April 21, 2026 · United Radiology

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.

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

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

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.

Tips to Solve Linear Equations Like This

Start by combining like terms on each side.
Aim to get all x terms on one side and constants on the other.
Never forget: whatever you do to one side, you must do to the other to maintain equality.
Practice with different numbers and signs to build confidence.

Want to Try More?

Use this method as a template:

Move variables to one side
Move constants to the other
Simplify and isolate x

Try equations like 2x + 7 = 3x – 1 or 5 – x = 2(3x + 6) to sharpen your skills.

Conclusion

Solving 3x – 4 = x + 5 shows that algebra is approachable and rewarding. With practice, you’ll not only find x = 4.5 easily — you’ll develop a strong foundation for mastering all types of equations. Keep practicing, stay curious, and remember: every equation tells a story waiting to be solved!

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