Set 40 − 15(n−1) < 1 → 40 − 15n + 15 < 1 → 55 − 15n < 1 → −15n < −54 → n > 54/15 = <<54/15=3.6>>3.6 - Sterling Industries
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
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:
📰 Since the remainder is 0, the last non-zero remainder is 26. 📰 A tech startup uses machine learning models trained on datasets of sizes $18$ MB and $42$ MB. To standardize preprocessing, they wish to divide each dataset into equal-sized blocks with no leftover data. What is the largest possible block size in MB? 📰 The largest block size that divides both 18 and 42 evenly is the greatest common divisor of 18 and 42. 📰 18 Wheels Of Steel American Long Haul 📰 Red Widow Necklace Is This Spider Killer Inspector Your New Obsession 4864734 📰 Zombie Island Chaos Scooby Doos Scariest Mystery Yet 2036304 📰 Dolus Suffocates This Suv Hides A Sin You Never See Coming 7854430 📰 Recommended Games On Steam 📰 Burning Mac 📰 Single Spaced 📰 How To Order A New Debit Card 📰 Recommended Electric Toothbrush 7330541 📰 Alle Must Know How To Make A Epic Book In Minecraft You Wont Believe The Sudden Twist 6221297 📰 Watch Wimbledon Like Never Beforeheres How To Never Miss A Moment 6233023 📰 Pizza Chain Chapter 11 📰 Windows Xp Reg Cleaner 📰 Sites That Stream Tv 📰 March 6Th ZodiacFinal 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
