x + (x+2) + (x+4) = 102 \quad \Rightarrow \quad 3x + 6 = 102 \quad \Rightarrow \quad 3x = 96 \quad \Rightarrow \quad x = 32 - Parker Core Knowledge
Solving the Equation: x + (x + 2) + (x + 4) = 102 Step-by-Step Breakdown
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
Understanding the Context
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: \( 2 + 4 = 6 \)
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Key Insights
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 \( x \)
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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.
See also:
- How to Solve Linear Equations
- Mastering Algebra: Step-by-Step Techniques
- Practice Problems for Algebra Beginners
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