Solve each inequality. Give the solution set in interval notat...

Question

Solve each inequality. Give the solution set in interval notation. 8x-3x+2<2(x+7)

Accepted Answer

Hey, everyone in this problem, we are asked to find the solution set for the following inequality and were told to express the answer in interval notation. And the inequality were given is nine X minus two, X plus five is less than four times X plus two. Now rewriting this nine X minus two, X plus five is less than four times X plus two, we were asked to solve for a solution set of an inequality. What it's really asking us to do is find all of the X values that satisfy this inequality. And in order to do that, we need to isolate X, we're going to do this just like we do with an equal sign. Okay. When we have an equation with an equality, we're going to get all the X terms collected on one side, we're gonna get all the constant terms collected on the other side in order to isolate for X. So let's start by expanding the right hand side here and simplifying we have nine X minus two X on the left hand side, that's gonna give us seven X and then we have plus five is less than on the right hand side, we have four times X plus two. We need to distribute the four to both of those terms. And so we get four X plus eight. Let's move the X terms to the left hand side and the constant terms to the right hand side. We have seven X minus four X. That's going to give us three X on the left hand side is less than on the right hand side. we have positive eight. We need to subtract five to move the five to the right hand side, just like we would do in an equation with an equal sign. And we get three on the left hand side. The last step, we just need to divide by three to isolate X. We get X is less than one and that's it. That's our solution set for the inequality. These are all of the X values as long as X is less than one, it's going to satisfy the inequality. Now, we're asked to write this an interval notation. We want X less than one. So the upper bound on our interval is going to be one. We have strictly lesson, we don't have less than or equal to. And so we want to round bracket to indicate that we don't include exactly one and this is just going to go from negative infinity, okay. Any value less than one, so any value all the way down to negative infinity is fine. We always use a round bracket when we're writing infinity. And so that is going to be our solution set in interval notation. And if we look at our answer choices that's going to correspond with answer A, we have the interval from negative infinity up to one, not including the end points. Thanks everyone for watching. I hope this video helped see you in the next one.

Solve each inequality. Give the solution set in interval notation. 8x-3x+2<2(x+7)

Key Concepts

Solving Linear Inequalities

Combining Like Terms

Interval Notation

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