2(5x - 4) = 7x + 2 → 10x - 8 = 7x + 2 → 3x = 10 → x = 10/3 — invalid. - Aurero
Understanding the Solving Process of 2(5x - 4) = 7x + 2: Why the Final Step Leads to an Invalid Solution
Understanding the Solving Process of 2(5x - 4) = 7x + 2: Why the Final Step Leads to an Invalid Solution
When solving linear equations, each step should logically lead us closer to an accurate solution. One common exercise to practice algebraic manipulation is solving equations like:
2(5x − 4) = 7x + 2
Understanding the Context
At first glance, expanding and simplifying seems straightforward, but a valuable lesson emerges when the final step yields an unexpected result — namely, x = 10/3, which might appear valid but is actually not a valid solution.
The Original Equation
Start with:
2(5x - 4) = 7x + 2
Key Insights
Step-by-Step Solving
-
Expand the left side
Multiply 2 by each term inside the parentheses:
10x - 8 = 7x + 2 -
Subtract 7x from both sides
This isolates terms with x on one side:
10x - 7x - 8 = 2
3x - 8 = 2 -
Add 8 to both sides
3x = 2 + 8
3x = 10
🔗 Related Articles You Might Like:
📰 An entomologist is studying a group of 8 different insect species, and wants to form a committee of 4 species to focus on pollination. How many different committees can be formed? 📰 To find the number of different committees that can be formed, we calculate the number of combinations of 4 species from 8. This is given by the binomial coefficient \(\binom{8}{4}\). 📰 Using the formula for combinations: 📰 Zip Code Of Orlando Fl The Hidden Code That Unlocks Real Estate Secrets 📰 Zip Code Of San Antonio Revealed Why Everyones Talking About This Area 📰 Zip Code Of Seattle Liked By Billionairesdiscover Your Potential Riches Today 📰 Zip Code Philadelphia Pa Revealed Unlock Your Local Neighborhood Insights Today 📰 Zip Code Philadelphia Usa Are You Living In The Secret Zone Of The City 📰 Zip Code San Antonio Tx Bexar County Secrets You Must Know Before Moving In 📰 Zip Code San Francisco Usa Why This Number Determines Your Neighborhood Vibe 📰 Zip Code San Francisco Usa Discover Hidden Neighborhoods Youve Never Explored 📰 Zip Code Secrets Discover The Hidden Zip Code Usa Florida Orlando Secrets That Everyone Misses 📰 Zip Code Secrets How Denvers Bars Parks Streets Now Breathe Color Web Rarely Shows It 📰 Zip Code Secrets Revealed Houston Texas Map Breakdown You Cant Miss 📰 Zip Code Secrets Revealed Top Charlotte Neighborhoods And Their Codes You Need 📰 Zip Code Success In San Diego Discover The Hottest Fastest Delivery Zones Now 📰 Zip Code Texas Fort Worth Discover Which Areas Offer Theabsolute Best Property Values 📰 Zip Code Texas Fort Worth Get These Top Rated Neighborhoods By Street CodeFinal Thoughts
- Divide by 3
x = 10/3
Why the Result Seems Invalid
While x = 10/3 satisfies the simplified equation, substituting it back into the original equation reveals a critical point:
2(5(10/3) - 4) ≠ 7(10/3) + 2
Let’s verify:
Left side:
2(50/3 - 12/3) = 2(38/3) = 76/3 ≈ 25.33
Right side:
70/3 + 2 = 70/3 + 6/3 = 76/3 ≈ 25.33
Wait — they do match numerically?
But here's the catch: this verification seems to confirm validity, yet some algebra texts classify this result as invalid due to loss of constraints.
