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

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.

8x - 11 ≤ 3x - 13

Accepted Answer

Hello. Today we're going to be solving the given inequality and representing its solution in interval notation and grabbing the graphing the solution. So what we are given is six X -7 is less than or equal to two X -16. 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're going to do is subtract two X to both sides of this inequality and add seven to both sides. And this is going to give us four. X is less than or equal to negative nine. Now, what we want to go ahead and do is get X by itself. So we're going to divide both sides of this inequality by positive four and this is going to give us X is less than or equal to negative 9/4. And we're going to leave it as a fraction because four doesn't evenly divide into nine. So we're gonna take this inequality and we're going to graph it on a number line. So we first draw a number line and we're going to put negative nine, number four in the middle of the number line. Now, what this inequality is saying is that we want all the numbers X to be less than negative 9/4 and it can be equal to negative 9/4. So we want all the numbers that come before negative 9/4 or in other words we want all the numbers that approach negative infinity. And this inequality allows us to include negative 9/4 in our solution set. So we're going to include negative 9/4. And we represent that with a solid dot on the number line. And since we want all the numbers that come before negative nine or four, we're going to shade in the whole left hand side of this number line. And this is going to be the graph of the inequality. Now let's go ahead and represent this an interval notation. We first start by writing the lowest number in our solution set and in this case here the lowest number is going to be negative infinity. Now, negative infinity doesn't have a finite value to it. So we're just going to assign it a parentheses. And we're going to close this interval notation by writing our biggest number which is negative 9/4. And since we're including negative 9/4, we're going to give it a bracket. And this is going to be the interval notation of the solution of the inequality. And the option that accurately represents both of these is going to be C. So c is the solution to this problem. So, I hope this video helps you in approaching this type of 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. 8x - 11 ≤ 3x - 13

Key Concepts

Linear Inequalities

Interval Notation

Graphing on a Number Line

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