That's enough of the basic ones. Those are all like saying chocolate ice cream is greater than vanilla. Pretty straightforward, right? Okay, maybe in some circles.
Solve One-Step Linear Inequalities - Grade 6 - Practice
Let's solve some basic linear inequalities, then try a few more complicated ones. Just as with linear equations, our goal is to isolate the variable on one side of the inequality sign.
Algebra - Linear Inequalities - Lamar University
Here's a trickier one: 8 x - 6 9. Let's start by adding 6 to both sides. Now we have 8 x 65. What do we do? Remember, it's just like a linear equation. If we had 8 x = 65, we'd divide both sides by 8. We do the same thing here. That gives us x 5. That's it!
Linear Inequality: Solving, Graphing & Problems - Video
Greater than and less than. These two symbols can be quite controversial. It all depends on what you put on either side. What if I said hot sauce is greater than ketchup? Or, cats are less than dogs? Or, the Denver Broncos are greater than the New England Patriots? These are debatable points. I mean, I think they're all true, and I'd argue them passionately, but they're really just opinions.
But, what if I said 6 7? Well, that's just wrong. 6 7. And, so are other numbers, including 5, 9, 8. well, the list just goes on from there. There's no debate. And, in this lesson, we're going to practice handling these types of situations.
Let's do one more basic one: x + 66 69. This time, we subtract 66 from both sides, which gives us x 8. If we graph that, we get this line:
But, then there are linear inequalities. A linear inequality is a linear expression that contains relational symbols. That means that instead of =, you'll see , , , or . So, instead of our variable standing in for a single value, it's standing in for a relational value, as in x 7, where x is all values greater than 7.
Note that we fill in the circle around the 8 because x isn't just less than 8, it's less than or equal to 8. X could be all these values as well as 8 - no sense making 8 feel left out.
First, what about this: x + 5 9. We treat this just like we would if we had x + 5 = 9. We subtract 5 from both sides. Now we have x 9. On a number line, that would look like the image below, where x is all numbers larger than, but not equal to, 9.
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