3(50 - 2y) + 2y \leq 90 \\

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.

$Construct an appropriate triangle to complete the table. (0^\circ \leq ...$

Image Gallery

$Construct an appropriate triangle to complete the table. (0^\circ \leq ...$

$algebra precalculus - Range of values for $y$ given $-2 \leq x \leq 3 ...$

Solved Subject to: 3X+2Y≤50 X+2Y≤302X−Y≤18Y≥4X≥0 and Y≥0 | Chegg.com

Solved ⎩⎨⎧−5x−3y≤−50−2x+3y≤17x+2y≤84x≥0y≥0 | Chegg.com

$Given: \text{Max } C = 2x+10y\\ 5x+2y\leq 40\\ x+2y \leq 20\\ y\geq 3 ...$

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:

📰 how long do dissolve stitches take to dissolve 📰 what jowls 📰 mucus feces human 📰 How To Prtscn On Windows 7980288 📰 American Rebel 6121446 📰 Discover The Secret Feature Inside The 2019 Jeep Cherokeeland That Leaves Everyone Mesmerized 6928927 📰 You Wont Believe What The Intel Graphic Command Center Can Do 4189230 📰 Actors Of Soul Plane 4315339 📰 Meaning Of Paralysed 2798117 📰 Wells Fargo Bank Severna Park Md 8024141 📰 5X12 5960148 📰 Hhs Chief Of Staff Exposed Inside The Surprising Secrets Of Americas Top Health Official 5290693 📰 Powerball For May 28Th 4922012 📰 The Haven They Found In Despair No Escape From Dusekkars Hands 6649720 📰 The Surprising Truth Ask And Ye Shall Receivedont Miss It 8361488 📰 Delta Skymiles Nerdwallet 8966389 📰 Download The Chime Appyour Phones New Best Friend For Sound Alerts And Joy Everyday 6917868 📰 Best Free Budgeting Apps 2025 4193435

Final 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.