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.
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.
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.
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
Knowing how to solve linear equations like this isn’t just about math homework. It strengthens your problem-solving skills, supports logic development, and prepares you for algebra, calculus, and applied sciences. From budgeting and physics to computer programming and engineering, linear equations model real-life relationships.
Bonus Tips: Quick Check
Always verify your solution by plugging x = –1/5 back into the original equation.
Left side:
4(–1/5) + 6 = –4/5 + 30/5 = 26/5
Right side:
–(–1/5) + 5 = 1/5 + 25/5 = 26/5
Both sides equal 26/5, confirming the solution is correct.
Conclusion
Mastering simple linear equations like 4x + 6 = -x + 5 opens the door to more complex mathematics. Practice simplifying both sides, moving variables, and isolating x — and remember, checking your work ensures accuracy. Keep solving, keep learning, and let algebra empower your problem-solving skills!
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