Graphing and Writing Inequalities - Example 4
Graphing and Writing Inequalities - Overview
Solve Absolute Value Inequalities - Example 1
Solve Absolute Value Inequalities - Example 2
Solve Absolute Value Inequalities - Example 3
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Graphing and Writing Inequalities - Example 3


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in this example, but being asked to write an inequality to represent the solution sets given in the following number ones. So let's take a look. Number one. So we're given a number line and we've already been graph the solution set. We want to come up with what inequality would represent a number line with the given shaving. So the first thing I recommend is always start with a variable, we have X. Then you need to figure out Well, what number are we getting or what is going to be our kind of what I'd like to call our key number? Meaning, Where does your circle happened On the number line? Our circle happens at one, so we know our values gonna have to be one. So now we just have to determine which of our inequality symbols we need to use. So let's first look at our shaving. We're shaving values that are to the right of one. Well, are these values that are to the right of one greater or less in one? Well, that would mean they're greater than so. That means we're gonna have a greater than symbol. The second thing we have to determine is should this be a greater than sign or greater than or equal to sign? Well, that comes down to Is one a solution? Well, it's not a solution, which is why there's an open circle. So when there's an open circle, you won't have your it or equal to part. So we've now written are inequality. The number line network given represents the solution set toe when X is greater than one. Now let's try number two. So again, we're going to start with our variable X. Then we're gonna put our key point, which in this case, is where our circle is. And at this point for this example, is that negative too? So now we have to determine which of our four inequality symbols is represented by our number one. Well, I see that our values that are shaded are to the left of negative, too. Well, are these values greater or less than negative, too? Well, that would mean they're less done, so we're gonna use are less inside. Then we have to determine should this just be a less than sign or should be a less than or equal to sign? Well, that all comes down to is negative to a solution and in this case it is, which is why there's a close circle. So we know that in this case we should use the less than or equal to sign. So what we found is that Inequality X is less than or equal to negative. Two represents the inequality or sorry, the number line that was graft for us.

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