So in this example, we're being asked to write it inequality to represent the given freeze. Then, after we do that, we're going to solve the inequality, and then we'll graph the solution set on the number line. So let's read our phrase here. It says a number increased by seven as at least 22. So let's break this down. First off, it's as a number. Well, we don't know what the number is. And in math, when we don't know a number, we can call it a variable so we can call this X now. The next phrase says, increased by will remember, increased by means to add. Well, what are we increasing this number by it says we're increasing it by seven now. This next phrase, it says, is at least so what is this phrase is at least mean Well, let's think about this. If I said you haven't least $10 that means that's the smallest amount you could have, or you could have anything larger than it. So therefore, when you see the phrase, at least this really means greater than or equal to, because the amount they tell you is the smallest value you could have. And again you could have it. That's why we have your equal to Or you could have anything larger. Well, what is it, at least? Well, it's at least 22. So now we've set up our numbers are inequality. So our inequality will be X plus seven is greater than or equal to 22. All right, now that we've written our inequality, let's go ahead and solve it. Well, to get X by itself, we're going to subtract seven from both sides. Well, 20 to minus seven is 15. So we're given that X is greater than or equal to 15. Okay, Perfect. Now we've solved. Now we just need to scrap our solution. Set on a number line. So we're going to set up our number line are critical. Number of 15 could go right in the middle. So now, first thing should be an open circle or close circle. Well, 15 could be a solution to this, so we're gonna have a close circle here. All right? The second thing should be shade to the left of the right. Well, because X could be greater than or equal to 15, that means we're going to shade to the right. So now, after we shade to the right, we have now solved our inequality and grafted solution set on a number line.