2(5x - 4) = 7x + 2 → 10x - 8 = 7x + 2 → 3x = 10 → x = 10/3 — invalid. - Decision Point
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:
📰 film bandslam 📰 film a walk on the moon 1999 📰 highlander the series 📰 Hbo Max Sign In Secrets You Cant Ignore Before The Door Closes 4762993 📰 Dow Jones Industrials 7310979 📰 Most Popular Apps On App Store 5011427 📰 Stop Steam Clogged Skin Forever Cetaphil Face Wash Secrets Revealed Inside 8123602 📰 Special Ops Season 2 9181558 📰 Top 7 Fathers Day Quotes Daily Fathers Feel Truly Celebrated 682269 📰 Penstation 9861275 📰 A Ladder 10 Meters Long Leans Against A Wall With Its Base 6 Meters From The Wall How High Up The Wall Does The Ladder Reach 6978765 📰 Mumbai Chhatrapati Shivaji International Airport 4195319 📰 White Cors Streak The Hidden Truth Behind Their Fashion Revolution 1213317 📰 This Simple Trick Reveals Fidelty Net Benefits You Cant Ignoreclick To Learn How 2747767 📰 Discover The Secret Water Shoes That Make Every Stroll By The Pool A Confidence Boost 4727404 📰 Carry On Dimensions For Delta 1649516 📰 6 Million Won To Usd Shocking 68M Swipewhy This Sudden Conversion Blow Could Change Your Life 9211774 📰 Whats Memory Cache Hiding No One Knows This Secretclick Here 1075924Final 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.
