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Question 209933: I recently just joined an algebra 2 class and the teacher gave me the homework from the past days but did not explain anything. I need help with 2 questions:
11. write the compound inequality that is represented by the graph:
<---------(-3)__________(1)---->
The circles around the numbers are both filled and the underscores represent the filled in line.
16. Graph the compound inequality:
2 less than or equal to x less than or equal to 5
Thank you so much if someone can explain these to me!!
Answer by tutor_paul(519)   (Show Source):
You can put this solution on YOUR website! 11. write the compound inequality that is represented by the graph:
<---------(-3)__________(1)---->
Since this is drawn just on one axis, all you have to care about is a single variable, lets call it 'x'.
If I am interpreting this correctly, you have a solid line drawn between the points -3 and 1. This represents the values that x can assume. Since the -3 and 1 are drawn as filled in circles, this means these numbers are included in the values that x can assume.
So what does this mean?
It means x can be -3. x can be 1. x can be anything between -3 and 1. In other words, x is greater than or equal to -3, AND x is less than or equal to 1.
To represent this with an inequality, you write it as:
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16. Graph the compound inequality:
2 less than or equal to x less than or equal to 5
This is poorly worded, however, I take it to mean:
Based on what we did in the first problem, you should be able to graph this. It's just a solid line between 2 and 5 with filled in circles on the 2 and 5.
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Note that is something is just "less than" rather than "less than or equal" and you are graphing, you do not fill in the the point with a solid circle; just draw an un-filled in circle (same applies to "greater than").
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God Luck,
tutor_paul@yahoo.com
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