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00:02: In this video, I'm gonna solve three X plus two is less than eight. So as you can see, this is an inequality because we have a less than sign, rather than an equals sign. And it is one variable because we only have the single variable "X". So we're solving a one-variable inequality. Now, how do I go about doing that? I pretty much do it the exact same way that I would solve a one variable equation, except instead of writing an equals sign, I'm gonna write the less than sign. So, we have three X plus two is less than eight. So my first step is to isolate my variable X. So in order to do that, I'm gonna subtract two from both sides. And I'm gonna get three X is less than eight minus two, which is six. And then I'm gonna divide both sides by three. So I get X is less than six divided by three, which is two. So now I have my solution: X is less than two. I'm gonna go ahead and graph the solution. And because this is a one-variable inequality, I'm not going to graph it on the coordinate plane, I'm gonna graph it on the number line. I'm in one dimension, so I'm gonna graph on the one-dimensional number line. 01:15: So I have the number line down here. X is less than two, so I need to find where the value two is on here. So, let's stick zero anywhere, and so here is two. Now notice it's just less than two, it's not less than or equal to two. So, at two, I'm gonna put an open circle and I'm not going to fill it in because two is not included. Now the solutions are all X values that are less than two. Less than means smaller than. So I'm going to shade to the left because I want all values that are less than, or smaller than, two.

This example is graphed on a number line since it contains one ______.
Responses
A variablevariable
B inequalityinequality
Question 2
What is the solution?
Responses
A x > 2x > 2
B x < 2x < 2
Question 3
True or False: An open circle was used on the graph because 2 was not included since it was not equal to.
Responses
A truetrue
B false

1 answer

Here are the answers to your questions based on the provided content:

Question 1: This example is graphed on a number line since it contains one ______.

  • Response: A. variable

Question 2: What is the solution?

  • Response: B. x < 2

Question 3: True or False: An open circle was used on the graph because 2 was not included since it was not equal to.

  • Response: A. true