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.

5x + 11 < 26

Accepted Answer

Hello today we're gonna be solving the given inequality and we're going to represent its answer in interval notation and graph the solution. So what we are given is three X plus Is less than 27. Now, in order to solve this inequality, we want to go ahead and get X by itself and in order to do that we can first subtract 15 to both sides of this inequality. Doing so is going to give us three. X is less than 27 minus 15 which is 12. And finally in order to get X by itself, we can divide both sides of this inequality by three and that's going to give us X is less than four. So this is the simplified version of our given inequality. Let's go ahead and graph this we first start by drawing a number line and we're going to put four in the middle of this number line. Now this inequality is saying that we want all the values of X that are going to be less than four. So we want all the numbers that come before four or in other words we want all the numbers that approach negative infinity. And since we only want the numbers that are going to be less than four, we are not going to include four in our solution set. So we're going to represent that on the number line with an open circle. Now, since we want all the numbers that come before four, we're going to shade in the left hand side of this graph and that's going to be the graph of the inequality. Now, let's go ahead and represent the solution in interval notation. We first start by writing the lowest number in our set solution or in other words the lowest number is going to be negative infinity. And since negative infinity doesn't have a finite value to it, we're going to close it off with the parentheses and that's gonna be approaching our biggest number in the solution set, which is going to be four. And since we are not including four in the solution set, we're going to close off this notation with the parentheses and this is going to be the interval notation of the graph. 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 understanding how to approach 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. 5x + 11 < 26

Key Concepts

Linear Inequalities

Interval Notation

Graphing on a Number Line

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