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.

3/4x + 10 = 7/8x.

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

Continue Reading

amazing world of gumball characters
amazo
amazo dc

🔗 Related Articles You Might Like:

📰 4; "The One-Step Method to Edit, Merge, and Save Any File as a Professional PDF!" 📰 5; "Download Faster, Save Better: The Best Tools for Making PDFs in Minutes!" 📰 You Won’t Believe How EASY It Is to Cancel PS Plus—Stop Feeling Stuck! 📰 Unsuspected Secret Hidden At Megaplex During Thanksgiving At Point Lehi 📰 Untouched Peaks Expose A Hidden World That Will Transform Your Soul 📰 Unveil The Secret Behind Mint Majesty Tea That Transformed Morning Rituals Forever 📰 Unveil The Secrets Behind Mission Bbqs Cancer Breaking Menu 📰 Unveil The Twisted Truth Behind Lystret No One Dared To Show 📰 Unveiled Forever The Day A Model Danced In Blazing Night 📰 Unveiled How Morticia Addams Stole The Spotlight In Her Eerie Costume 📰 Unveiled In Unsensational Nude Photo That Shocked Fans Everywhere 📰 Unveiled Michelle Pfeiffers Nude Shock Moment Rules Social Media 📰 Unveiled The Hidden World Of Media Bias Everyones Ignoring 📰 Unveiled The Mardi Gras Mask That Blurred Reality And Fantasy Forever 📰 Unveiling The Secrets Of The Maiden City Derrys Hidden Past 📰 Unveiling The Shocking Truth About Lustriva That Will Blow Your Mind 📰 Unwrap The Creamy Secret Ice Cream So Light You Almost Forget It Exists 📰 Unwrap The Mystery Behind The Legendary Mangajinx Manga Style Secrets

Final 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.

Verifying the Solution