3x + 2(10 - x) = 24 \Rightarrow 3x + 20 - 2x = 24 \Rightarrow x + 20 = 24 \Rightarrow x = 4 - 500apps
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:
📰 The Flag Of New Jersey Has A Secret Hidden In Plain Sight—You Won’t Believe What’s On It! 📰 Why The Old Jersey Flag Finally Got A Surprising Makeover You Haven’t Seen Before 📰 New Jersey’s Flag Just Ashamed You—What Exactly Did They Hide? 📰 The Tournament Of Power Explodesheres What Actually Happened 📰 The Town Monument You Thought Was Just Decorationheres What Lies Beneath 📰 The Toxel Evolution Explained What Every Consumer Needs To Know Now 📰 The Toyota 22R That Turns Tractors Into Legendary Off Road Machines Do You Want One 📰 The Trabeculae Carneae Mystery How This Microscopic Layer Powers Your Heart 📰 The Trail Boss Formula Transform Any Hike Into A Thrilling Adventure Today 📰 The Traitor Movie That Stunned Audiencesheres Why It Became A Cultural Phenomenon 📰 The Transformers Animated Movie Devggerate Fans Are Talkingis It Good 📰 The Transverse Plane Is The Secret Angle That Shapes Real Results Dont Miss This 📰 The Trappers Who Sold Out Everyoneheres What Theyre Hiding 📰 The Trilogy Of Terror 3 Stories That Will Keep You Up All Night Dont Miss This 📰 The Triumph Spitfire Automatic Just Went Viral Heres Why You Need One 📰 The Troll Meme Everyones Sharing Youll Want To See These Before They Go Viral 📰 The True Devastation Of Underworld Films Revealed You Need To See This 📰 The True Summer Color Palette Thats Taking Social Media Shop Now For The Must Have TonesFinal 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.
