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

józsef barsi
jørne
k map

🔗 Related Articles You Might Like:

📰 Monkey butt—nature’s butt-flexing explosives, and it’s unforgettable 📰 Moozi’s Secret reveals what no one dares to admit 📰 You won’t believe the hidden power in every Moozi sound 📰 App Hollister 722239 📰 Notdstrom Rack 2715339 📰 Gamecubes Hidden Gem The Iconic Mario Kart That Defined Fast Paced Racing 519070 📰 This Rare Sweet Red Wine Surprises Everyone With A Taste That Defies Logic 1845359 📰 Best Seasons Of Family Guy 3146740 📰 Discover The Secret Feature In Microsoft Windows Photo Gallery That Saves You Time 226368 📰 Rob Reiner Children Photos 4781655 📰 You Talkin To Me 8829861 📰 How A Joint Brokerage Account Boosts Your Financial Fidelity Overnight 3120464 📰 Herb Baumeister Pool 4481037 📰 Puzutask Com Final Call The Fight Against Confusion Just Ended 3437487 📰 Barry Sommers Wells Fargo 6138436 📰 Never Look Back Scan Smarter With The Ultimate Epson App For Windows 8328359 📰 How To Make Distilled Water At Home 7742058 📰 Sql Developer Mac 2137728

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