Question

Graph the three parts of inequality 1 < x + 3 < 9

Answer 1

First part:  1 is less than the sum of x and 3:  1 < x+3.
Second part:  the sum of x and 3 is less than 9.
Obviously 1 < 9.

Taking another look at 1<x+3, we can solve for x:  -2<x.  Draw a dashed vertical line thru x = -2.
Taking another look at x+3<9, subtract 3 from both sides.  Then x<6.
Draw a dashed vertical line thru x=6.

Shade the area between these two vertical lines to obtain the desired graph.