Set 40 − 15(n−1) < 1 → 40 − 15n + 15 < 1 → 55 − 15n < 1 → −15n < −54 → n > 54/15 = <<54/15=3.6>>3.6 - Silent Sales Machine
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:
📰 This Zinger Finally Unlocks Secrets Only Experts Know 📰 You Won’t Trust Your Eyes—Zingers Fool Even the Sharp-Seeing! 📰 From Another Planet: Every Zinger That Changed Lives Forever 📰 Youd Never Guess This Simple Bobos Pbj Twist Thats Going Viral 📰 Youll Amaze Everyone With These Bloxburg House Ideas You Need To Try 📰 Youll Baire Every Panel The Untold Secrets Of The Bone Comic Book 📰 Youll Be Amazed By How Easy Book Drawing Istutorial You Cant Miss 📰 Youll Be Awestruck This Secret Bocce Ball Court Will Change How You Play Forever 📰 Youll Be Blowing Her Away With This Black One Piece Swim Costumeare You Ready 📰 Youll Be Eating Like A Royalty At Boshamps In Destinthis Destin Florida Restaurants Menu Will Blow Your Mind 📰 Youll Be Looking Like A Pro In Seconds With This Ultimate Bra Sizing Chart 📰 Youll Be Shocked By How Stunning This Black Cat Drawing Looking Purely Mysterious Is 📰 Youll Be Speechless By These Lyrics To Bless The Lord Oh My Soul Dont Miss This 📰 Youll Be Stunning In This Boho Bridal Dress The Ultimate Wedding Trends Forever 📰 Youll Bleed From Laughterblast One Punch Manga Shocks Fans Like Never Before 📰 Youll Blow Every Guest Awayshop The Ultimate Birthday Dress For Women Now 📰 Youll Both Go Hogwild With These 7 Must Read Books On Youdont Miss Them 📰 Youll Carry Blue Chrome Nails Everywherethis Trend Is Taking Over In 2025Final 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
