Solving and graphing the compound inequalities?

Question

1.     x < 1 and x > -3

 

2.    x < 4 or x > 6

 

 

Answer 1

Because the signs include equal to signs, you will need to put filled in circles at the indicated points.

1.  Mark the two points of your number line at 1 and -3.  The line will go left from 1.  The line will go right from 3.  The overlapping area is the solution.  You should draw a line connecting 1 and -3.

 

2.  Mark the two points at 4 and 6.  The line from 4 goes to the left.  The line from 6 goes to the right.  Since this is an "or" inequality, whatever is covered by either of these lines is correct.  the only part of the number line that is not shaded is the area between 4 and 6.