Solving the Equation: x + (x + 2) + (x + 4) = 102 Step-by-Step Breakdown

Mathematics is full of elegant small problems with powerful solutions — and this equation is a perfect example. Whether you're a student learning algebra or someone brushing up on fundamental math skills, understanding how to simplify and solve expressions like \( x + (x + 2) + (x + 4) = 102 \) is essential. In this article, we’ll walk you through the step-by-step breakdown, solving \( x + (x+2) + (x+4) = 102 \) correctly, and highlight why this chain of reasoning matters.

Understanding the Equation

The equation in question is:\[x + (x + 2) + (x + 4) = 102\]Here, you have three expressions:- \( x \)- \( x + 2 \)- \( x + 4 \)

These are linear expressions involving the variable \( x \), forming a simple linear equation ready for simplification.

Step 1: Remove Parentheses and Combine Like Terms

Start by eliminating parentheses since all terms inside are enclosed in plus signs:\[x + x + 2 + x + 4 = 102\]Now combine like terms:- Combine the \( x \) terms: \( x + x + x = 3x \)- Combine constants: \( 2 + 4 = 6 \)

This simplifies the equation to:\[3x + 6 = 102\]

Step 2: Isolate the Variable Term

Subtract 6 from both sides to isolate the term containing \( x \):\[3x + 6 - 6 = 102 - 6 \implies 3x = 96\]

This step uses the fundamental algebraic principle of performing the same operation on both sides to maintain equation balance.

Step 3: Solve for \( x \)

Divide both sides by 3:\[3x = 96 \implies x = \frac{96}{3} = 32\]

Thus, the solution is:\[x = 32\]

Why This Problem Matters

Breaking down this equation reveals a core algebraic strategy: combining similar terms, simplifying expressions, and isolating variables. These skills are not only vital for algebra but also lay the foundation for solving real-world problems in science, engineering, economics, and data analysis.

Understanding such equations helps you decode patterns, predict outcomes, and build logical thinking — essential for anyone looking to grow their quantitative skills.

Final Thoughts

The equation \( x + (x+2) + (x+4) = 102 \) might seem straightforward, but mastering its solution teaches clarity and precision in mathematical reasoning. Always remember the four key steps: simplify expressions, combine like terms, isolate variables, and solve step-by-step. With practice, solving equations becomes intuitive — and the path from \( x + (x+2) + (x+4) = 102 \) to \( x = 32 \) is a great roadmap to clear, confident math comprehension.

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See also:- How to Solve Linear Equations- Mastering Algebra: Step-by-Step Techniques- Practice Problems for Algebra Beginners

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Meta Description:Learn how to solve \( x + (x+2) + (x+4) = 102 \) step-by-step — from simplifying expressions to finding \( x = 32 \). Perfect for students mastering algebra fundamentals.