Solving 4x + 6 = -x + 5: A Step-by-Step Guide to Finding the Solution

Solving linear equations like 4x + 6 = -x + 5 is a fundamental skill in algebra that helps build a strong foundation for more advanced math topics. Whether you're a student, teacher, or lifelong learner, understanding how to isolate variables is essential. In this article, we’ll walk through the process of solving the equation 4x + 6 = -x + 5, step by step, while explaining the key mathematical concepts involved.

Understanding the Context

What Is the Equation?

We begin with the equation:
4x + 6 = -x + 5

Our goal is to find the value(s) of x that make this equation true. To do so, we’ll use algebraic techniques to isolate the variable x on one side of the equation.

4x + 6 = -x + 5

Key Insights

Step 1: Move All Terms Containing x to One Side

To isolate x, first move all terms with x to the left side and constant terms to the right side.

Subtract -x from both sides (or add x to both sides):
4x + x + 6 = 5
→ 5x + 6 = 5

Alternatively, you can subtract 5 from both sides first:
4x + 6 - 5 = 0
→ 4x + 1 = 0
But combining constants first often simplifies the process.

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Final Thoughts

Step 2: Move Constant Terms to the Right Side

Subtract 6 from both sides:
5x = 5 - 6
5x = -1

Step 3: Solve for x

Now divide both sides by 5:
x = -1 ÷ 5
x = -1/5

Final Answer

👉 The solution to the equation 4x + 6 = -x + 5 is
x = –1/5

Why Learning This Matters – Real-World & Academic Relevance