2(5x - 4) = 7x + 2 → 10x - 8 = 7x + 2 → 3x = 10 → x = 10/3 — invalid. - High Altitude Science
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:
📰 bracers 📰 braces color 📰 braces colors 📰 You Wont Believe How Step By Step Perler Bead Masterpieces Transform Your Craft 📰 You Wont Believe How Sycamore Boobs Transform Any Moment 📰 You Wont Believe How The Bye Weeks Are Shaking Up The Nfl 2025 📰 You Wont Believe How The Nemesis System Outsmarts Even The Smartest Minds 📰 You Wont Believe How The New Balance 9060 Pink Changes Everythingpink Like Never Before 📰 You Wont Believe How The New Balance Rebel V4 Changed Everything 📰 You Wont Believe How These Heirlooms Define A True Old Money Look 📰 You Wont Believe How These Nail Designs Transform Short Nails Instantly 📰 You Wont Believe How These Nail Shapes Transform Your Hands Forever 📰 You Wont Believe How These Nails Look On This Glamorous Breakthrough Polish 📰 You Wont Believe How These Nb 574 Sneakers Transform Your Look 📰 You Wont Believe How These Off White Jordan 4S Transformed My Shoes Forever 📰 You Wont Believe How These Onions Transform In Pickled Onions Recipe 📰 You Wont Believe How These Paintball Guns Turn Ordinary Sessions Into High Intensity War Zones 📰 You Wont Believe How These Pearl Nails Transform Your Nail Game ForeverFinal 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.
