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

#### 5523.57A marine policy advisor is evaluating the sustainability of a fishery. If the total allowable catch (TAC) is 12,000 kg per year and the current catch is 8,400 kg, what percentage of the TAC is being utilized? How many kilograms over the TAC would the current catch be if it exceeded it by 15%?
A science policy analyst is reviewing a climate initiative that aims to reduce carbon emissions by 45% over 10 years. If the current annual emissions are 80 million metric tons, and the reductions are evenly distributed each year, how many million metric tons must be reduced annually to meet the target?
A robotics engineer is designing a robotic arm with three joints. The torque requirements are proportional to 2x, 3x, and 4x respectively, where x is a base torque value. If the total maximum torque capacity of the system is 540 Nm, what is the value of x?

🔗 Related Articles You Might Like:

📰 You Won’t Believe What These Golden Earrings Are Worth 📰 Hidden in Plain Sight: The Stunning Gold Earrings Everyone’s Crying Over 📰 Unlock the Secret Behind These Lightning-Strike Gold Earrings 📰 Notre Dame Stadium Seating Chart 2604869 📰 Bank America Cd Interest Rates 2823097 📰 X 3 1 1 157990 📰 Unlock The Secrets Of Normal Distribution Excel Boost Your Data Analysis Skills Today 6433253 📰 Hcps Calendar 1752371 📰 Yahoofi Hidden Features That Will Change How You Use Smart Features Forever 1048976 📰 Pilot Artificial Intelligence 9163673 📰 Pine Valley Gc New Jersey 127893 📰 Database System Meaning Explained The Simple Guide That Will Shock You With Its Simplicity 3330443 📰 Prime Brokerage 5183832 📰 Total Time 4 Hours 2 Hours 6 Hours 92668 📰 Breakthrough Discovery The Magic Of One Piece Fruits You Need To Try Today 5687591 📰 Finger Limes 4665751 📰 You Wont Believe How Burnjaro Reviews Became The Game Changer In 2024 2619899 📰 Gatorade Plastic Water Bottles 4693887

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