In Exercises 59–94, solve each absolute value inequality.

|x| ...

Question

In Exercises 59–94, solve each absolute value inequality.

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Accepted Answer

Hello everyone in this radio. We're going to be looking at this practice problem where we want to use interval notation to express the solution set for the inequality absolute value of X greater than five. So in this case when we have an absolute value of X. And see that X can be positive X. Or X can be negative X. So I'm going to use these two scenarios and solve for the inequality in both of these ways. So if X is positive then I have X is greater than five and that becomes my range or inequality. If I have negative X is greater than five, then I'm going to divide by negative to solve for X. So that's which is a sign of my inequality. So it's no longer greater than it's now less than And my five turns negative. So I have X is less than -5. So if I draw this on a number line, Say I have negative five over here and going up negative four, negative three, -2 -101234 five. And I sort of visualize these. So say I have the positive X. Is greater than five. I have an X. Here and it has to be greater. So I can draw an error going up and then I have X less than negative five. So at negative five. My X needs to be less than So you can see that I have sort of two intervals that I need to represent. So using this graph I have a negative infinity 2 -5 is my first range. And I can draw parentheses after the negative five because it's a in equal it's a less than and not less than or equal to or greater than or equal to if that makes sense. There's no equal to there's just a less than or greater than. And I need to do a union Because I still need to account for my second part over here where I have five to infinity. And again I can do the parentheses because it is a greater than and not unequal to. So this becomes the solution set for the inequality and you can see that this aligns with answer choice D. So hopefully this video helped and see you next time.

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