In Exercises 51–58, solve each compound inequality.

- 3 ≤ x - 2 ...

Question

In Exercises 51–58, solve each compound inequality.

- 3 ≤ x - 2 < 1

Accepted Answer

Hello today we're going to be solving the compound inequality. So the compound inequality given to us is negative five less than or equal to the quantity X minus four, which is going to be less than seven. Now, what it means to solve the compound inequality is we want to go ahead and isolate this variable X. And in order to do that we need to get rid of this negative four term. Well to to get rid of the negative four term. We're just gonna go ahead and add four to all sides of this compound inequality. So negative five plus four is going to give us negative one and that's going to be less than or equal to the quantity X minus four plus four which is going to leave us with X. And that's going to be less than seven plus four which is going to be 11. So since we've isolated the variable X, we've solved the compound inequality. So the compound inequality is the set of solutions including negative one and everything between negative one and 11. And that means that the answer to this problem is going to be B So I hope this video helps you in understanding how to solve the compound inequality and I'll go ahead and see you all in the next video

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