3x + 2(10 - x) = 24 \Rightarrow 3x + 20 - 2x = 24 \Rightarrow x + 20 = 24 \Rightarrow x = 4 - Get link 4share
Solving the Linear Equation: 3x + 2(10 − x) = 24
Solving the Linear Equation: 3x + 2(10 − x) = 24
Understanding how to solve linear equations is a fundamental skill in algebra—essential not only for academics but also for real-world problem-solving. In this comprehensive guide, we will walk step-by-step through the solution of the equation:
3x + 2(10 − x) = 24
The Original Equation
Start with the equation:
3x + 2(10 − x) = 24
Understanding the Context
Step 1: Expand the Parentheses
The first step is to eliminate the parentheses. Multiply 2 across the terms inside:
3x + 2 × 10 − 2 × x = 24
Which simplifies to:
3x + 20 − 2x = 24
Step 2: Combine Like Terms
Combine the x-terms on the left side:
(3x − 2x) + 20 = 24
This gives:
x + 20 = 24
Step 3: Isolate the Variable
Subtract 20 from both sides to solve for x:
x + 20 − 20 = 24 − 20
Therefore:
x = 4
Final Answer
The solution to the equation 3x + 2(10 − x) = 24 is:
x = 4
Key Insights
Why This Matters: Real-World Applications
Linear equations model everyday scenarios such as budgeting, mixing solutions, or comparing costs. Mastering their solution helps build logical reasoning and analytical thinking—skills useful in science, engineering, economics, and more.
Alternative Problem: Why 3x + 2(10 − x) = 24 Matters
This particular equation forces us to simplify and combine like terms, a common step in more complex algebraic manipulation. Practicing this helps students recognize patterns and improve speed and accuracy.
Practice Problems to Master
Try solving these equations like the example above:
- 5x + 3(8 − x) = 27
- 2(4 + x) − 3x = 10
- 4(x − 1) + 5x = 25–₴
Summary
Solving 3x + 2(10 − x) = 24 follows standard algebraic steps: expand, combine like terms, isolate x. The clear process demonstrates how simplification unlocks the solution. Whether for homework or future challenges, proficiency in linear equations opens doors to deeper mathematical mastery.
🔗 Related Articles You Might Like:
📰 Unlock Timeless Elegance: The Ultimate Black Wallpaper That Dominates Every Room 📰 Dark & Stylish: Black Wallpaper That’s Taking Interior Design by Storm! 📰 You Won’t Believe How Stunning This Black Formal Gown Looks on Her! 📰 Kick Aas Movie The Shocking Secret Behind His Fitness Legend Mysteriously Revealed 📰 Kids 3D Printer Revolution Watch Your Child Create Toys Gadgets At Home 📰 Kids Love These Fun Food Gamesget Your Little Chef Cooking Today 📰 Kids Umbrellas That Wont Get Lost The Ultimate Rain Protection For Little Adventurers 📰 Kill Me Baby The Shocking Twist You Never Saw Coming This One Will Change You 📰 Killington Trail Map Secrets To Every Hidden Trail You Must Hike 📰 Kindergarten Sight Words That Guarantee Reading Confidencestart Now 📰 King Geedorah Unleashed The Legendary Pokmon That Will Shock You 📰 King Von Dreads Unleashed The Shocking Truth Behind This Iconic Rap Myth 📰 Kinky Twist Hairstyles That Will Never Fail To Surprise 📰 Kirby Deluxe Triple Unlock The Ultimate Power Bonk Attack 📰 Kirby Planet Robobot The Ultimate Battle Against Unbeatable Robots 📰 Kirby Robobot Awakens The Ultimate Battle Against Robots Pixels 📰 Kirby Wallpaper Magic Transform Your Space Like A Pixel Perfect Nintendo Fan Only Here 📰 Kirbys Dream Buffet Insta Worthy Desserts Youll Want To Eat FirstFinal Thoughts
Keywords: linear equations, solving equations, algebra, 3x + 2(10 − x) = 24, step-by-step solution, algebra tutorial, x = 4, math practice, solving equations with parentheses, algebra basics
Meta Description: Learn how to solve 3x + 2(10 − x) = 24 step-by-step. Discover the solution x = 4, review key algebra techniques, and practice similar equations for better math skills.
