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: \( 2 + 4 = 6 \)

1. $ {x}{x} x+60°$ $ 3x$ $360° = 3x + x + | StudyX

Image Gallery

1. $ {x}{x} x+60°$ $ 3x$ $360° = 3x + x + | StudyX
How do you Integrate (\int x^2e^{x^3}dx) - YouTube
(x, y) \in R \quad \Rightarrow \quad x+4 y=10 \text { but }(y, z) \in R\..
(x, y) \in R \quad \Rightarrow \quad x+4 y=10 \text { but }(y, z) \in R\..
\Rightarrow \quad\left(x^{2}+3 x+2\right)-\left(x^{2}-4 x+3\right)=12+1

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 \( x \)

Continue Reading

Solving equations 1 and 2: From 1, $ a = 5 - 3b $. Substituting into 2: $ 2(5 - 3b) + 4b = 6 \Rightarrow 10 - 6b + 4b = 6 \Rightarrow -2b = -4 \Rightarrow b = 2 $. Then $ a = 5 - 6 = -1 $.
Solving equations 3 and 4: From 3, $ c = 7 - 3d $. Substituting into 4: $ 2(7 - 3d) + 4d = 8 \Rightarrow 14 - 6d + 4d = 8 \Rightarrow -2d = -6 \Rightarrow d = 3 $. Then $ c = 7 - 9 = -2 $.
Thus, $ \mathbf{M} = \begin{pmatrix} -1 & 2 \\ -2 & 3 \end{pmatrix} $. Final answer: $ \boxed{\begin{pmatrix} -1 & 2 \\ -2 & 3 \end{pmatrix}} $.

🔗 Related Articles You Might Like:

📰 The REVOLUTIONARY New ZOMBIES Map for Bo6 Will Change How You Survive Forever – Here’s the Knockout! 📰 You Won’t Believe What’s in the Latest Mission Impossible Movie! SPOILER READY! 💥 📰 The NEW Mission Impossible Film Shocks the World—This One Will Change Everything! 📰 Stunning Fact 1 Inch Is Surprisingly Equal To How Many Centimeters Find Out 📰 Stunning Gameplay Unlocked Everything You Need To Know About Console 2Ds Nintendo 📰 Stunning Pool Terrible Deckcan These Specialists Restore It Fast Click To Learn 📰 Stunning Shades Of Color Marron You Cant Miss In Interior Design 📰 Stunning Short Curls Master The Curling Wand In Minutes 📰 Style That Drove The Crowd Wild Insider Secrets Of The Country Concert Outfit 📰 Style Your Windows Instantly The Ultimate Curtain For Rod Guide Inside 📰 Stylish Compact The Cropped Puffer Jacket You Cant Stop Posting About 📰 Substitute D 1 Into 1 3 And 4 📰 Substitute Into B 5A 25 A 15 Rightarrow 4A 25 15 Rightarrow 4A 1 Rightarrow A Frac14 📰 Substituting S 8 📰 Substituting T 4 📰 Subtract 5 📰 Subtracting 1 From Both Sides X 4 📰 Success Inside Every Stitch Topistinant Crochet Tops That Slay

Final Thoughts

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

Keywords: solve linear equation, algebra 101, step-by-step equation solving, x + (x+2) + (x+4) = 102, equation simplification, math problem solving, isolating variables, algebra tutorial for beginners