So in this section we're gonna actually start solving linear inequalities. So this section we're just gonna talk about solving inequalities, using addition and subtraction. Well, what I want to show you is that solving inequalities is very similar to solving equations. So take a look at our first example. We have X minus five is equal. Deny. Well, remember to solve for X. We simply need to add five to both sides of our equation because then the negative five and positive five cancel out. So we're left with X equals well, nine plus five is 14. So notice in this case by us saying that X is equal to 14. There's Onley one solution The Onley value for X That will make that equation true is 14. Now let's go to our second example we have X minus five is less than nine. So the same idea If we're trying to isolate X, this is kind of just like a one step equation. So the solve for X, what we're going to dio is we're gonna add five to both sides of our inequality. Well again, nine plus five is 14, but this time we're given our solution as X is less than 14. Well, how are these two different? Well, the solution saying X is less than 14 means if we plug in any value for X, that is less than 14, it will make our original inequality true. So that's the difference between equation and inequality in equation. We just have this one specific answer as the posted inequalities. We're gonna have multiple answers. Now let's go to number three. We have X minus five is less than or equal to nine again. We want to isolate the variable. So to do this, we're gonna add five to both sides of our equation. So are negative. Five and positive five. Cancel. We've already mentioned nine plus five is 14, so we have X is less than or equal to 14. And as we've already mentioned in previous sections, how is this answer different than number two? Well, the answer from number three says that X is less than or equal to 14, meaning any number that's less than 14. If we substitute into our inequality will be true, or if we substitute 14 into our inequality, it will also be true. So it has all the same answers as number two, except we can also include 14. All right, let's solve the number four. X minus five is greater than nine again. It doesn't matter that it's now a greater than sign. We're going to still add five to both sides of our inequality. So we're left with exes, but this time greater than 14. So in this case, any value that's bigger than 14. If we were the substituted in place effects in our original and equality would make a true statement. But remember, 14 would not work in this particular case, so it's anything that's greater than it not equal to. And in the last example we have, X minus five is greater than or equal to nine again. Inequality sign Doesn't MATTER. We're still just going to add five to both sides of our inequality. So we're left with X is greater than or equal to 14. So again, what's the difference between the answer and four versus five? And number 5 14 is included in solution set as opposed to a number 4 14 is not included. So as you can see, solving inequalities is going to be just like solving equations three. Only difference is the solutions. We're gonna have multiple solutions, so what you'll find is you'll typically represent your solution. Set using a number line so over the next couple of examples will go through the process of solving inequalities and graphing the solution set on a number line.

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## Video Transcript

So in this section we're gonna actually start solving linear inequalities. So this section we're just gonna talk about solving inequalities, using addition and subtraction. Well, what I want to show you is that solving inequalities is very similar to solving equations. So take a look at our first example. We have X minus five is equal. Deny. Well, remember to solve for X. We simply need to add five to both sides of our equation because then the negative five and positive five cancel out. So we're left with X equals well, nine plus five is 14. So notice in this case by us saying that X is equal to 14. There's Onley one solution The Onley value for X That will make that equation true is 14. Now let's go to our second example we have X minus five is less than nine. So the same idea If we're trying to isolate X, this is kind of just like a one step equation. So the solve for X, what we're going to dio is we're gonna add five to both sides of our inequality. Well again, nine plus five is 14, but this time we're given our solution as X is less than 14. Well, how are these two different? Well, the solution saying X is less than 14 means if we plug in any value for X, that is less than 14, it will make our original inequality true. So that's the difference between equation and inequality in equation. We just have this one specific answer as the posted inequalities. We're gonna have multiple answers. Now let's go to number three. We have X minus five is less than or equal to nine again. We want to isolate the variable. So to do this, we're gonna add five to both sides of our equation. So are negative. Five and positive five. Cancel. We've already mentioned nine plus five is 14, so we have X is less than or equal to 14. And as we've already mentioned in previous sections, how is this answer different than number two? Well, the answer from number three says that X is less than or equal to 14, meaning any number that's less than 14. If we substitute into our inequality will be true, or if we substitute 14 into our inequality, it will also be true. So it has all the same answers as number two, except we can also include 14. All right, let's solve the number four. X minus five is greater than nine again. It doesn't matter that it's now a greater than sign. We're going to still add five to both sides of our inequality. So we're left with exes, but this time greater than 14. So in this case, any value that's bigger than 14. If we were the substituted in place effects in our original and equality would make a true statement. But remember, 14 would not work in this particular case, so it's anything that's greater than it not equal to. And in the last example we have, X minus five is greater than or equal to nine again. Inequality sign Doesn't MATTER. We're still just going to add five to both sides of our inequality. So we're left with X is greater than or equal to 14. So again, what's the difference between the answer and four versus five? And number 5 14 is included in solution set as opposed to a number 4 14 is not included. So as you can see, solving inequalities is going to be just like solving equations three. Only difference is the solutions. We're gonna have multiple solutions, so what you'll find is you'll typically represent your solution. Set using a number line so over the next couple of examples will go through the process of solving inequalities and graphing the solution set on a number line.

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