2(5x - 4) = 7x + 2 → 10x - 8 = 7x + 2 → 3x = 10 → x = 10/3 — invalid. - inBeat
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
Image Gallery
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:
📰 \[ 15 \times 6 \times 6 = 540 \] 📰 Calculate the total number of ways to choose any 4 markers from the 24 available markers (6 in each category): 📰 \[ \binom{24}{4} = \frac{24 \times 23 \times 22 \times 21}{4 \times 3 \times 2 \times 1} = 10,626 \] 📰 Ukraine And Russia 2122737 📰 5S Attention Barbara Edens Untold Naked Legacy Shocks Fans Forever 2214527 📰 Oura Ring Near Me 6144445 📰 Shocking Emtala Law Breakdown What Hospitals Wont Tell You Free Legal Insights Inside 9732952 📰 How To Record Audio On Powerpoint 1836179 📰 Rockstar Games Stock 2184351 📰 Hotel Pet Friendly 1952719 📰 Actual Transparent Window 1703322 📰 Youd Never Guess What Downloading This Game Unlockedclick To Find Out 6480826 📰 College Board Question Bank 7841633 📰 Zip Code Usa Las Vegas Unlock Property Values Neighborhood Insights More 7246953 📰 Girl Bikini Thats Redefining Summer Fashion Perfect For Every Body Type 8010036 📰 Typical Renters Insurance Cost 9208219 📰 Apple Stocks Outstanding 2158941 📰 Best Simulation Games 5692934Final 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.
