In all exercises, other than exercises with no solution, use i...

Question

In all exercises, other than exercises with no solution, use interval notation to express solution sets and graph each solution set on a number line. In Exercises 27–50, solve each linear inequality. 2x - 11 < - 3(x + 2)

Accepted Answer

Hello today we're going to be solving the given inequality. Then we're gonna graphics solution and represent the solution in interval notation. So what we are given is five X minus nine is less than two times the quantity X plus three. Now, in order to simplify the inequality, the first thing we're gonna want to do is to distribute two into the quantity X plus three. This is going to give us five, X minus nine is less than two, X plus six. Now, what we want to go ahead and do is move all the X terms to one side of the inequality and all the non X terms to the other side. So what we can go ahead and do is subtract two X to both sides of the inequality And add 9 to both sides. And doing this is going to give us three, X is less than 15. Now we want to go ahead and get X by itself and in order to do that we can divide both sides of this inequality by three and that's going to give us X is less than five. So this is the simplified version of our inequality. Let's go ahead and graph this inequality now. So we first start off by drawing our number line and we're going to put five in the middle of this number line. Now, what this inequality is saying is we want all the numbers X to be less than five. So we want all the numbers that come before five or in other words we want all the numbers that approach negative infinity and X can only be less than five. So we're not including five in our solution set. So we can represent that with an open circle on our number line. And again, once we want all the numbers less than five, so we're gonna be shedding in the left hand side of our number line. And this is going to be the graph of our inequality. Now let's represent our inequality in interval notation. We first start off by riding the lowest number of our of our solution set, which in this case is going to be negative infinity. And since negative infinity doesn't have a certain value to it, we're going to put a parentheses next to it. Next we're going to write our biggest value which is five. And since we are not including five in our solution set, we're going to put a parentheses e next to five. And this is going to be the interval notation of our graph. And among the options given to us the option that accurately represents this graph and the interval notation is going to be a So a is the solution to this problem. So, I hope this video helps you in understanding how to approach this inequality problem. And I'll go ahead and see you all in the next video

In all exercises, other than exercises with no solution, use interval notation to express solution sets and graph each solution set on a number line. In Exercises 27–50, solve each linear inequality. 2x - 11 < - 3(x + 2)

Key Concepts

Solving Linear Inequalities

Interval Notation

Graphing Solution Sets on a Number Line

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