How do you write a linear inequality from a word problem?

Cracking the Code: Turning Word Problems into Linear Inequalities (No Sweat!)

Okay, so linear inequalities might sound intimidating, but trust me, they’re just a fancy way of saying “things aren’t always equal.” Think of it like this: life isn’t always about finding that one perfect answer. Sometimes, it’s about figuring out a range of possibilities. That’s where inequalities shine! We use them all the time to model real-world stuff where things can vary – like how much money you need, or how many hours you can work.

So, what are these linear inequalities, anyway? Well, unlike those strict linear equations you might remember from algebra (where there’s only one right answer), inequalities give you a whole bunch of solutions. They use symbols like < (less than), > (greater than), ≤ (less than or equal to), and ≥ (greater than or equal to) to show relationships.

For example, if I say “x > 5,” I mean x can be anything bigger than 5. 6, 7, 8, a million – you name it! But not 5 itself. It’s like saying you need more than five bucks to buy that fancy coffee. On the flip side, “y ≤ 10” means y can be 10, or anything less than 10. Think of it as a speed limit: you can go up to 10 mph, but not over!

Now, the tricky part: how do you take a real-world problem described in words and turn it into one of these inequalities? Don’t worry; I’ve got you covered.

From Words to Math: Your Step-by-Step Guide