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.

5(x - 2) - 3(x + 4) ≥ 2x - 20

Accepted Answer

Hello, today we're gonna be solving the linear inequality then expressing the solution in interval notation. So what we are given is three times the quantity X minus four minus two times the quantity X plus six greater than or equal to X minus 10. Now, the first thing we're gonna want to do is we're gonna want to simplify the left hand side of the inequality. In order to do this, we're going to distribute three into X minus four and we're going to distribute negative two into X plus six. Three times X is going to give us three X and three times negative four is going to give us negative 12, negative two times X is going to give us negative two X and negative two times six is going to give us negative 12 and this is going to be greater than equal to X minus 10. Now, what we wanna do is you want to combine the light terms on the left hand side, we can combine three X and negative two X and we can combine both of the negative twelves. This is going to simplify the left hand side to give us X minus 24 that is greater than equal to X minus 10. Now, what we wanna do is we want to get all of the X terms to one side of the inequality and all of the constants to one side of the inequality. What we can do is we can add 24 to both sides of the inequality and subtract X to both sides of the inequality that is gonna leave us with zero is greater than equal to 14. But this is a false statement which means that there is no solution to this inequality. And with that being said, the answer to this problem is going to be D so I hope this video helps you in understanding how to approach this 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. 5(x - 2) - 3(x + 4) ≥ 2x - 20

Key Concepts

Linear Inequalities

Interval Notation

Graphing on a Number Line

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