-3<x<=5 graph on number line

Question

i dont get inequalities and graphing them on num. lines

Answer 1

The inequality tells us that the number x lies in between -3 and 5.  5 is included in the line.

 

Draw a number line that is labeled with the numbers -3 and 5 on it.  Draw an open circle at -3 and draw a closed circle at 5.  Once you have your two circles, connect them by drawing a line between them.

 

 

*Closed circles on a number line means that the number is included in the set.

Answer 2

We represent graphs on a number line by shading or darkening the regions that are possible for x.

 

In this case -3<x would be a graph with an open circle at x=-3 to represent that x cannot be -3, and have all numbers to the right of -3 shaded or darkened on the number line.

 

To graph x<=5, we would mark the point x=5 with a filled in closed circle, to represent that x=5 is possible, and shade all numbers to the left of 5, to represent x<5 on the number line.

 

The complete graph of the inequality you have given is represented as an intersection of these two sets (meaning x must satisfy BOTH of these individual, single inequalities).  To find this intersection graphically, we look for points that have been shaded in BOTH of our pictures...namely all the points to the right of -3, not including -3, that are also to the left of 5, including 5.

 

We draw this on a number line by first drawing a line and marking 0 with a slash and label, then mark -3 with an open circle and 5 with a closed circle, and darken the liner between these two circles!

 

Hope that helps...if you'd like to see a picture, we can use WyzAnts online tutoring and I can draw it for you during a tutoring session!