In Exercises 51–58, solve each compound inequality. - 3 ≤ (2/3...

Question

In Exercises 51–58, solve each compound inequality. - 3 ≤ (2/3)x - 5 < - 1

Accepted Answer

Welcome back. I'm so glad you're here. We've got this compound inequality meaning it's got more than two parts here. We've got negative nine is less than or equal to one third X minus three is less than negative six. And what we want to do is solve for X. We want to get X by itself in the middle. How do we do that? It's just like solving for X when there's an equation or inequality. We want to get X by itself by moving the negative three and the one third and we're going to go through that same process. But what we do to one side in this case, well what we do to one part of it, we have to do to all three parts. So we want to clear out that negative three. We're going to add three but we add it to all three parts here. So on the left negative nine plus three that's a negative six is less than or equal to one third X. And now that negative three plus three cancels out in the middle is less than negative six plus three, that's negative three. Great. This X is almost by itself here. What we want to do next is get rid of the one third. So we're going to multiply it by three because one third times three that's just one. So the X will be one X. Or X. But what we do to one part we have to do to the whole thing to all three parts. So on the left we've got negative six times three. Well that's negative 18 is less than or equal to and as we said, one third times three is just one. So now it's X in the middle is less than negative. Three times three is negative nine while we look at our answer choices and that matches with answer choice. A well done, we'll catch you on the next one.

In Exercises 51–58, solve each compound inequality. - 3 ≤ (2/3)x - 5 < - 1

Key Concepts

Compound Inequalities

Solving Linear Inequalities

Interval Notation and Solution Sets

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