3/4x + 10 = 7/8x. - Dyverse
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:
📰 Heart-Stopping Moment When The Dress Shimmered Like Real Magic! 📰 Mexico Guerrero Uncovered: Secrets No One Wants You to Know 📰 What Lies Beneath the Surface in Mexico Guerrero—You’re Not Ready to Believe 📰 This Dragons Crown Strategy Will Change How You Play Foreverclick To Discover 📰 This Dragons House Hunting Adventure Will Shock Youyou Wont Believe Which Home He Found 📰 This Drake Album Cover Shocked Everyoneyoull Never Guess The Hidden Secret Inside 📰 This Drake Dragon Moves Differentlyscientists Are Obsessed 📰 This Drake Hoodie Is Hanging Everywhereheres Why You Need One Now 📰 This Drake Wallpaper Will Make Your Wall Glowno One Else Has Done It Like This 📰 This Dralf Moment Will Leave You Speechless Dont Click Stop Reading 📰 This Dreamcast Controller Will Make You Demand Ityoull Never Buy Again 📰 This Dreamer Dc Trick Actually Traps Your Darkest Nightmaresstop Reading 📰 This Dredd Actor Just Stole Hollywoodwatch How He Became A Pop Culture Phenomenon 📰 This Dredd Movie Scene Shattered Fans Expectations Heres The Shocking Truth 📰 This Dress Bandage Bandage Dress Is Changing How You Dress Forever 📰 This Dress Blues Secret Will Make You Buy It Tonight 📰 This Dress By Elsa Changed Fashion Forevershop Like A Queen Instantly 📰 This Dress Changed Everything The Drop Waist Trend Every Bride DeservesFinal 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.
