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.

Solved 3. 8.3 x 10+4.6 x 10 4. 9.5 x 10-7.7 x 10 5. 5.5 x | Chegg.com

Image Gallery

Solved 3. 8.3 x 10+4.6 x 10 4. 9.5 x 10-7.7 x 10 5. 5.5 x | Chegg.com
Solved: Solve: 3x-10=x+8 [Math]
Solved 10x-3=8+10x | Chegg.com
[ANSWERED] 7 4 x 8 2 10 4x 12 8 X X 4 10 11 3x 1 13 9 5 x 10 3 12 6x 10 ...
3.4×10-7 is between which two numbers?1×10-9 and | Chegg.com

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

hardbound vs paperback
hardcore henry hardcore henry
hardcore leveling warrior

🔗 Related Articles You Might Like:

📰 cobb lee j 📰 welcome back carter cast 📰 barney fishwick 📰 Prezzee Leaked Real Users Are Raving About These Life Changing Price Cutsdiscover How 9330071 📰 Gluten Free Pancakes That Taste Just Like The Real Thing 1315862 📰 Raised Garden Lumber Thats Been Treated For Maximum Growth Zero Rot 6330631 📰 Party Bus Nashville 3282260 📰 John Herbert Dillinger First National Bank 7432979 📰 The Shocking Netbenefits Of Fidelity Investmentssecrets To Wealth Growth Revealed 4250513 📰 Absolutely Irresistible The Smoked Chuck Roast That Mirrors Perfect Barbecue Smoke 7974476 📰 Your Fios Tv Plan 9412763 📰 Java 23 Released In September 2025Prepare For The Future Of Java With These Game Changing Tools 1291817 📰 La La Land Cast 7782209 📰 Tjx Shares Are Hitting All Time Highswhat You Need To Know Before Its Too Late 259912 📰 Frankentest 10 Revealed This Mmorpg Redefines Fantasy Gaming Forever 2044848 📰 Can One Tattoo Redefine A Mans Destiny Mannens Mark Does 8463028 📰 Shocking Underline Techniques You Need To Master For Flawless Highlighting 599109 📰 Altima Car 2010 Shocked Enthusiastsheres The Shocking Upgrade Youre Missing 729922

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