3(50 - 2y) + 2y \leq 90 \\ - inBeat
Understanding the Inequality: 3(50 - 2y) + 2y ≤ 90
A Comprehensive Breakdown for Beginners with Solving Strategies
Understanding the Inequality: 3(50 - 2y) + 2y ≤ 90
A Comprehensive Breakdown for Beginners with Solving Strategies
Introduction
Mathematical inequalities play a crucial role in solving real-life problems, optimizing resources, and modeling constraints—especially in algebra. One common type is linear inequality, such as:
Understanding the Context
3(50 - 2y) + 2y ≤ 90
At first glance, this inequality may seem complex, but with a step-by-step approach, anyone can simplify, solve, and interpret it. Whether you're studying math in school, preparing for standardized tests, or applying algebra to practical scenarios, understanding how to work with such expressions is invaluable. In this article, we’ll break down the inequality, solve it systematically, and explore its real-world implications.
Step 1: Simplify the Expression
We begin by expanding and combining like terms in the expression 3(50 - 2y) + 2y ≤ 90.
Image Gallery
Key Insights
Expand the parentheses:
3 × 50 = 150
3 × (-2y) = -6y
So,
3(50 - 2y) = 150 - 6y
Now substitute back:
150 - 6y + 2y ≤ 90
Combine like terms:
-6y + 2y = -4y
So the inequality becomes:
150 - 4y ≤ 90
🔗 Related Articles You Might Like:
📰 moses christian bale 📰 steve cohen 📰 the movie grand budapest hotel 📰 Kristen Dunst 6169169 📰 Children Of The Corn 1984 Theatrical Trailer 2181879 📰 How A Forgotten Gmc At4 Just Changed Everything For Truck Lovers Forever 672869 📰 From Ceo Reveals To Cutting Edge Demosoracle Convention 2025 Delivers In The Clickbait Style 5467015 📰 Is Cloudworld 2025 The Breakthrough Technology That Will Rewrite The Cloud Revolution 9185661 📰 Unlock Your Brains Full Potential With These All Time Best Puzzle Gamesgame Changing 9530313 📰 1942 Penny Value Soaringwe Discovered What This Little Coin Could Buy 4551820 📰 Why The Us Currency Is Crashingare You Ready For The Economic Shock 3537856 📰 How Old Was Melania When She Married Donald Trump 3664750 📰 Define Compare 195096 📰 Todays Belh Price Breakthrough Is The Market In Desperation Or Discovery 1104453 📰 Isla Vistas Hidden Secrets That Will Shock Your Life 5533220 📰 4D Explained In 60 Secondsdiscover The Hidden Dimensions Mastering Physics 1451111 📰 Trump Reveals Secrets How He Cured Autism In Just 7 Daystested Now 4208331 📰 Discover Kenya Like Never Beforeclick To Explore The Complete Map Of Kenya And Hidden Gems Inside 4117510Final Thoughts
Step 2: Isolate the Variable Term
Next, subtract 150 from both sides to isolate the term with y:
150 - 4y - 150 ≤ 90 - 150
Simplify:
-4y ≤ -60
Step 3: Solve for y
Now divide both sides by -4. Remember: dividing or multiplying both sides of an inequality by a negative number reverses the inequality sign.
y ≥ (-60) ÷ (-4)
y ≥ 15
Final Solution
The solution to the inequality 3(50 - 2y) + 2y ≤ 90 is:
y ≥ 15
What Does This Mean?
This result tells us that y must be 15 or greater to satisfy the original inequality. In practical terms, if y represents a measurable quantity—such as a daily limit, production unit, or cost factor—this constraint ensures values stay within acceptable bounds.
For example:
- If y is the number of items produced per day, production must be ≥15 units daily to meet capacity or regulatory limits.
- In budgeting, if y stands for spending beyond a base 50 minus cost terms, then spending 15 or more results in a balanced or acceptable financial outcome under the model.
Visual Interpretation: Number Line Representation
In inequality graphs, y ≥ 15 is shown as a line crossing 15 with a closed circle (indicating inclusion) and shading to the right, representing all values greater than or equal to 15.
