# In mathematics, a compound inequality is an inequality involving two or more inequalities connected by logical operators such as "and" and "or". Compound inequalities can be written in many ways. For example: 2x+3 or 5x+5 >10

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All right. So for this example, we're being asked to write the compound inequality to represent a given phrase. And then we're gonna graph the solution set on the number one. So let's take a look at our freeze here. Were given that all real numbers less than seven and greater than or equal to negative five. Well, the first part says we're talking about numbers that are less than seven. So how would we write in inequality for this? Well, we would simply have X is less than seven. Now, the key word here is an an statement, so we'll use the word. And so what is the second part? Say it says that were greater than or equal to negative five. So that means X could be greater than or equal to negative five. So this is one perfectly good way to write our inequality here. Now, remember, we could also rewrite it as just one, um, compound inequality without using the word. And so we're going to start with our smallest value, which is the negative five, and we're gonna flip it around. So in other words, I'm gonna put the negative five first in the X second. But remember, that means my inequality sign also must flip so it become less than or equal to. So now, when we write our compound inequality, we're gonna start with the smaller value. So we're gonna have negative five is less than or equal to x. And remember, X could be less than seven. So we're gonna have X is less than seven. So this is another way we could write the same compound inequality. Okay, so now the next thing we need to dio is graft a solution set. So we're going to set up our number line. We're gonna put our key values on here. We have negative five and seven and negative five. We're gonna have a close circle because it's less than or equal to X and at seven will have an open circle because it's strictly less than X or X is less than seven. So remember, kind of like, what are inequality shows? X is in between negative five and seven. So that's gonna be the same thing on a number line. We're going to shade in between negative five and seven. So this would be all the real numbers that are less than seven and at the same time are greater than or equal to negative five

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