Set 40 − 15(n−1) < 1 → 40 − 15n + 15 < 1 → 55 − 15n < 1 → −15n < −54 → n > 54/15 = <<54/15=3.6>>3.6 - IQnection
Understanding the Inequality: Set 40 – 15(n – 1) < 1 Step-by-Step Breakdown
Understanding the Inequality: Set 40 – 15(n – 1) < 1 Step-by-Step Breakdown
Solving inequalities is a foundational skill in algebra, especially when analyzing relationships between variables—especially real-world applications like best-case scenarios, break-even analysis, or performance benchmarks. One common but often confusing form is:
> Set 40 – 15(n – 1) < 1
Understanding the Context
Understanding how to manipulate this inequality correctly unlocks deeper insight into linear relationships and helps solve problems efficiently. In this article, we’ll break down this inequality step-by-step to clarify each transformation, arrive at the correct solution, and explore its practical meaning.
Step-by-Step Explanation
Let’s dissect the original inequality:
Set 40 – 15(n – 1) < 1
Image Gallery
Key Insights
Step 1: Expand the parentheses
Start by distributing the −15 across the expression inside the parentheses:
> 40 – 15(n – 1) = 40 – 15n + 15
(Because –15 × –1 = +15)
Now the inequality becomes:
40 – 15n + 15 < 1
Step 2: Combine like terms
🔗 Related Articles You Might Like:
📰 You Wont Believe What Happens When You Open Port 3389—Shocking Network Hack Alert! 📰 3389 Port Revealed: The Hidden Gateway Hackers Love (Use With Extreme Caution!) 📰 Why Open Port 3389? Experts Expose Its Dark Secrets (Shocking Results Inside) 📰 A Patent Attorney Is Assessing Infringement Risks Across 80 Active Patents 35 Are Utility Patents 25 Are Design Patents And 40 Are Provisional Filings If 15 Of Utility Patents And 10 Of Provisional Filings Are Deemed High Risk How Many High Risk Patents Are There In Total 4200269 📰 Foxcatcher Movie 741658 📰 Bryony Hannah 2365145 📰 Average Interest Rate On Car Loan 9626994 📰 Sexy Asseaa Exposed Why Every Moment Feels Like A Hot Secret 7588348 📰 6 7 6 7 1321403 📰 The Surprising Truth About Rolling Over Your 401K You Never Readcould You Lose 50K Easily 8672671 📰 Youll Earn 5000 Just By Referring Friends To Fidelitys Referral Bonus Program 7316094 📰 You Wont Believe How My Favorite Black Clover Characters Will Change The Entire Story 7505317 📰 Dennys Senior Menu With Prices 8047596 📰 From Little Grants To Massive Support Strike Big With Bard Grants Today 2470418 📰 System Interrupts System Interrupts 185800 📰 Motorpoint Just Dropped The Deal That Everything Motorsport Enthusiasts Are Obsessed With 5962795 📰 Boost Your Care With Iu Health Patient Portalget Instant Access To Records Appointments 8488194 📰 Nakobe Dean Injury 2581949Final Thoughts
Combine the constant terms on the left-hand side:
40 + 15 = 55
So,
55 – 15n < 1
Step 3: Isolate the term with n
Subtract 55 from both sides to move the constant to the right:
–15n < 1 – 55
–15n < –54
Step 4: Solve for n
Now divide both sides by −15. Important: When dividing or multiplying both sides of an inequality by a negative number, you must reverse the inequality sign:
> n > (–54) ÷ (–15)
n > 54/15
Now simplify the fraction:
54 ÷ 15 = 3.6
So,
n > 3.6
