3/4x + 10 = 7/8x. - Get link 4share
Understanding and Solving the Equation: 3/4x + 10 = 7/8x
Understanding and Solving the Equation: 3/4x + 10 = 7/8x
Mathematics often presents challenges, especially when solving for variables in linear equations. One common type of problem involves isolating the variable x in expressions with fractions. In this article, we’ll explore how to solve the equation 3/4x + 10 = 7/8x step by step, explain the key algebraic concepts, and provide practical tips for correcting such equations—whether you're doing homework, preparing for exams, or simply expanding your math skills.
Understanding the Context
Solving the Equation: Step-by-Step Guide
Step 1: Understand the equation
We start with:
3/4x + 10 = 7/8x
Our goal is to isolate x on one side. This requires manipulating both sides using inverse operations while preserving equality.
Key Insights
Step 2: Eliminate the fractions by finding a common denominator
Both coefficients of x—3/4 and 7/8—are fractions. To simplify, express them with a common denominator (8):
- 3/4 = 6/8
- 7/8 already has denominator 8
Rewriting the equation:
(6/8)x + 10 = (7/8)x
Step 3: Subtract (6/8)x from both sides
🔗 Related Articles You Might Like:
📰 damon herriman movies and tv shows 📰 damon wayans jr movies and tv shows 📰 damp pokemon 📰 Discover The Hidden Secret Of Nude Sandals That Anyone Should Be Wearing 📰 Discover The Hidden Secret Of Panes Con Pollo Salvadororeosyou Wont Believe How Tender They Are 📰 Discover The Hidden Secrets Of Norarosejean You Wont Believe What Shes Accomplished 📰 Discover The Hidden Secrets Of Pac Man Machine Arcade Totally Game Changing 📰 Discover The Hidden Secrets Of Your Body Parts Essential Facts For Everyone 📰 Discover The Hidden Superfood Pad Kra Pow That500 Power Up Your Health Overnight 📰 Discover The Hidden Superhero Of The Sea Pangasius Bocourti Fish Youve Never Heard Of 📰 Discover The Hidden Treasures In The Pampered Chef Catalog Cook Like A Celebrity Chef Today 📰 Discover The Hidden Treasures Of Oficinas Before Everyone Does 📰 Discover The Hottest New Nintendo Switch 2 Games Creating Hype Nationwide 📰 Discover The Hottest Nude Nail Trends That Are Taking Social Media By Storm 📰 Discover The Hottest One Piece Memes Thatll Make You Lol Out Loud 📰 Discover The Iconic Pan De Bono Trick That Guarantees Morning Joyclick To Learn 📰 Discover The Legendary Omega Ruby Roma Sparkling Scandal Thats Taking The Market By Storm 📰 Discover The Legendary Onimusha The Ultimate Way Of The Sword That Will Blow Your MindFinal Thoughts
This isolates the constant on the left and terms with x on the right:
10 = (7/8)x – (6/8)x
10 = (1/8)x
Step 4: Solve for x
Now solve:
x = 10 × 8
x = 80
Final Answer
The solution to 3/4x + 10 = 7/8x is
x = 80
Why This Equation Matters: Key Concepts
- Linear Equations: This is a first-degree equation—meaning x appears only to the first power—common in algebra and physics applications.
- Fractions & Common Denominators: Converting fractions to a common denominator simplifies arithmetic and avoids errors.
- Balancing Techniques: Any operation (addition, subtraction, multiplication) applied to one side must be applied to the other to maintain equality.
