3(50 - 2y) + 2y \leq 90 \\ - Coaching Toolbox
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:
📰 Mind-Blowing: Tether Gold Surges to $100,000—What It Means for Investors! 📰 Breaking: Tether Gold Just Broke $50K—Why Its the Hottest Crypto Asset Today! 📰 This Texting App for PC Will Revolutionize How You Text Forever! 📰 Pim Pictus 9552844 📰 You Wont Believe Whats Inside Fidelity Productsyoull Want To See This 2256232 📰 Rocket League Tournament 2354536 📰 Unmasking The Fear The Shocking Nuclear Bomb Radius Map Youve Never Seen 6075895 📰 Getaway Shootout Chaos Firefights Flash And Balance Of Power 4495432 📰 The Uncovered Truth About Sep Ira Contribution Limitsbreak The 76500 Limit Today 3492711 📰 This Original Snow White Story Looks Different Than You Remembercan You Spot The Differences 3695996 📰 The Shocking Secret About Hoopa You Didnt Know Dont Miss It 5839699 📰 Bride Living 1642624 📰 Youre Not Prepared Heres Your Copilot Readiness Assessment To Find Out 5464756 📰 A Car Travels 60 Miles 9298867 📰 This Lucky Duel Casino Shocked Everyonewatch The Outcomes Law Of Luck In Action 7464804 📰 You Wont Believe The Shocking Difference Between Malt And Shakesee How They Compare 3616454 📰 Goog Vs Googl Stock The Matchup That Shocked Investors Forever 2424437 📰 Whats The Right Heart Rate For A 2 Year Old Experts Reveal The Normal Range 9624023Final 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.
