Solving Absolute Value Inequalities - Example 3

An inequality is a mathematical statement that one quantity is less than or greater than another quantity. If the statement is true for all possible values of the quantities, then the inequality is said to be "satisfiable", "valid" or "truthful"; otherwise it is said to be "unsatisfiable", "invalid" or "false".

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Video Transcript

the compound inequality of seven Tom's. The absolute value of Ian over three modest non is less than 12. So before we begin working it, we need to simplify and get the absolute value of an over three by itself. So let's go ahead and add non to both sods. So seven times the absolute value of in over three is less than 21. From here, we can divide both sides by seven. So that means that the absolute value of in over three is less than three. Now that we have a simplified, we can go ahead and start working. So the absolute value of an over three is less than three. So we need to work this out twice, So we'll have in over three is less than three. We need to multiply both sides by the denominator. So that leaves me with Ian is less than not. The second time I work it I'm gonna have in over three is greater than negative three. Again. We're gonna multiply both sides by the denominator. So I'll have in is greater than negative nine. So now we need to decide what kind of inequality this ISS. So we have in is less than non and an is greater than negative now. So if I draw a number line and I'm just going to put my nonce down so since since they're both same number itself, we can just look at him from this angle. So we have in is less than nods. Open circle, going to the lift. And we have N is greater than negative nine. Open circle going to the right. I can see that this is an and statement because they're going to The arrows were going towards each other. So another way of writing that is negative non is less than in, which is less than nine.