Solve Compound Inequalities - And Statements - Example 4
Solve Compound Inequalities - And Statements - Overview
Solve Compound Inequalities - Or Statements - Example 1
Solve Compound Inequalities - Or Statements - Example 2
Solve Compound Inequalities - Or Statements - Example 3
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Solve Compound Inequalities - And Statements - Example 3


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So in this example being asked to solve the given compound inequality, I never gonna graphics solution set on the number line. So take a look at this. Inequality were given an an statement that's all written as one inequality. So what our goal is is to get X all by itself in the middle. So almost what you want to do is treat this like a regular inequality. So what, we have to move first? Well, you would wanna move that seven by subtracting seven, but in this case, we have to subtract seven from the left hand side from the middle and from the right hand side, you have to make sure you do it from each side. Okay, let's see what happens. Well, negative five minus seven is negative. 12. We'll bring down our lesson sign now. In the middle, we have seven minus seven. This will cancel, so we just have to acts. Then we'll bring our in the qualities down in the quality sign down. Then we have 11 minus seven, which is for okay. Well, we still have to get X by itself. Well, X is getting times by two. So to undo it we need to divide again. The left hand, middle and right hand side by two. Well, negative 12 Divided by two is negative. Six. We'll bring down our inequality sign the two cancels. So we just have X and we'll bring down our in the quality side again. And then we have four divided by two, which is two so perfect. We have now solved the compound inequality. So we found that negative six is less than necks and at the same time, X is less than two. Okay, now we just need to graft a solution set on a number line. So we'll set up our number line. We'll start with negative six and then to in both cases that we're gonna have open circles because X is greater than negative six. And it's less than two not equal to him. And just as it is in our compound, in the quality exes in between negative six and two, which bringing represented a number line by shading in between the two values. So now we have solved and graft to giving compound inequality. So remember when they give it to you as one statement all at once, your goal is to get X by itself or whatever variable they give you in the middle. But remember, if you do something to move, if you go to move something from the middle, you have to make sure you do it from each side of the inequality.

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